Упр 1, страница 135, часть 2 - гдз по алгебре 10 класс учебник Пак, Ардакулы

Часть 2. Глава 7. Случайные величины и их характеристики. Параграф 3. Числовые характеристики дискретных случайных величин. Задачи - страница 135.

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App\Models\Task {#1030 // resources/views/models/task/default.blade.php
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          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1119426
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119
              #items: array:1 [
                0 => App\Models\Term {#1116
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Часть"
                      "field_creative_case" => "Частью"
                      "field_dative_case" => "Части"
                      "field_genitive_case" => "Части"
                      "field_nominative_case" => "Часть"
                      "field_prepositional_case" => "Части"
                    ]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #original: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Часть"
                      "field_creative_case" => "Частью"
                      "field_dative_case" => "Части"
                      "field_genitive_case" => "Части"
                      "field_nominative_case" => "Часть"
                      "field_prepositional_case" => "Части"
                    ]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1148
              #items: array:1 [
                0 => App\Models\Book {#1118
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 4295
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1120
                      #items: array:1 [
                        0 => App\Models\Term {#1117
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6471
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алгебра"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "алгебру"
                              "field_creative_case" => "алгеброй"
                              "field_dative_case" => "алгебре"
                              "field_genitive_case" => "алгебры"
                              "field_nominative_case" => "алгебра"
                              "field_prepositional_case" => "алгебре"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "algebra"
                          ]
                          #original: array:10 [
                            "id" => 6471
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алгебра"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "алгебру"
                              "field_creative_case" => "алгеброй"
                              "field_dative_case" => "алгебре"
                              "field_genitive_case" => "алгебры"
                              "field_nominative_case" => "алгебра"
                              "field_prepositional_case" => "алгебре"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "algebra"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1121
                      #items: array:1 [
                        0 => App\Models\Term {#1122
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5459
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "10"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "десятый"
                              "field_creative_case" => "десятым"
                              "field_dative_case" => "десятому"
                              "field_genitive_case" => "десятого"
                              "field_nominative_case" => "десятый"
                              "field_prepositional_case" => "десятом"
                            ]
                            "field_translit" => "desjatyj"
                          ]
                          #original: array:6 [
                            "id" => 5459
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "10"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "десятый"
                              "field_creative_case" => "десятым"
                              "field_dative_case" => "десятому"
                              "field_genitive_case" => "десятого"
                              "field_nominative_case" => "десятый"
                              "field_prepositional_case" => "десятом"
                            ]
                            "field_translit" => "desjatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123
                      #items: array:1 [
                        0 => App\Models\Term {#1124
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 7006
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алматыкітап баспасы"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "almatykitap baspasy"
                          ]
                          #original: array:6 [
                            "id" => 7006
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алматыкітап баспасы"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "almatykitap baspasy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1125
                      #items: array:3 [
                        0 => App\Models\Term {#1126
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 7007
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Пак"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Олег"
                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 7007
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Пак"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Олег"
                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1127
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 7008
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ардакулы"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Дархан"
                            "field_patronymic" => null
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 7008
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ардакулы"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Дархан"
                            "field_patronymic" => null
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        2 => App\Models\Term {#1128
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 7009
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ескендирова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Елена"
                            "field_patronymic" => "Викторовна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 7009
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Ескендирова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Елена"
                            "field_patronymic" => "Викторовна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130
                      #items: array:1 [
                        0 => App\Models\Term {#1131
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1132
                      #items: array:1 [
                        0 => App\Models\Term {#1133
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 6994
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Казахстан"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "kazakhstan"
                          ]
                          #original: array:6 [
                            "id" => 6994
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Казахстан"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "kazakhstan"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1134
                      #items: array:1 [
                        0 => App\Models\Term {#1135
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 6995
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алматы"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "almaty"
                          ]
                          #original: array:6 [
                            "id" => 6995
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Алматы"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
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                            ]
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                          ]
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                          ]
                        }
                      ]
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                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1136
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1137
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140
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                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1141
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                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
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                    "field_part" => "1, 2"
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                    "field_for_whom" => "Учебник для учащихся 10 класса общеобразовательной школы общественно-гуманитарного направления"
                    "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан"
                    "field_reserve_field" => null
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                    "field_tasks_count" => "1063"
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                    "field_default_folder" => "/algebra_10/baspasy-u19/"
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                    "field_cover" => array:1 [
                      0 => "/media/algebra_10/baspasy-u19/covers/cover1.webp?ts=1752152865"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/algebra_10/baspasy-u19/covers/cover1.webp?ts=1752152865"
                        "alt" => ""
                        "width" => "1940"
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                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1142
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                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1143
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1144
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1145
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
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                    "breadcrumbs" => array:3 [
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                    ]
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1120}
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                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129}
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                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139}
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                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140}
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                    "field_reserve_field" => null
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                    "field_cover" => array:1 [
                      0 => "/media/algebra_10/baspasy-u19/covers/cover1.webp?ts=1752152865"
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                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1142}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1143}
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                    "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1145}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
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                    "breadcrumbs" => array:3 [
                      "class" => 381
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                    ]
                  ]
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                  #attributeCastCache: []
                  #dateFormat: null
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                  #dispatchesEvents: []
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                  #visible: []
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                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
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            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146
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              #escapeWhenCastingToString: false
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          ]
          #original: array:24 [
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            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119}
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            0 => "*"
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        }
        1 => App\Models\Branch {#1147
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          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
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          #attributes: array:24 [
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            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Случайные величины и их характеристики"
            "field_branch_order" => "7"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1152
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                0 => App\Models\Term {#1149
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
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                  #perPage: 15
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                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
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                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
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                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
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                      "field_accusative_case" => "Главу"
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                      "field_genitive_case" => "Главы"
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                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
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                  ]
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                  #attributeCastCache: []
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                  #fillable: []
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                    0 => "*"
                  ]
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              ]
              #escapeWhenCastingToString: false
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              ]
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            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150
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              ]
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          ]
        }
        2 => App\Models\Branch {#1153
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          #primaryKey: "id"
          #keyType: "int"
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            "created_at" => "2026-04-10 13:58:26"
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                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
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                  #perPage: 15
                  +exists: true
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                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
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                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
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                      "field_dative_case" => "Параграфу"
                      "field_genitive_case" => "Параграфа"
                      "field_nominative_case" => "Параграф"
                      "field_prepositional_case" => "Параграфе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
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                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
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                      "field_prepositional_case" => "Параграфе"
                    ]
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                    "field_short_name" => "§"
                  ]
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                    0 => "*"
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                }
              ]
              #escapeWhenCastingToString: false
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                0 => App\Models\Branch {#1164
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
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                      #escapeWhenCastingToString: false
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            "field_branch_order" => "3"
            "field_url" => null
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            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1156}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1165}
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          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        3 => App\Models\Branch {#1158
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1120522
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Задачи"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "135"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
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            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1161
              #items: array:1 [
                0 => App\Models\Book {#1118}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174
              #items: array:1 [
                0 => App\Models\Branch {#1173
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1120521
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Числовые характеристики дискретных случайных величин"
                    "field_branch_order" => "3"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1175
                      #items: array:1 [
                        0 => App\Models\Term {#1154}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_page_start" => "134"
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                    "field_navigation_title" => null
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                    "field_h1" => null
                    "field_description_top" => null
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                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1176
                      #items: array:1 [
                        0 => App\Models\Book {#1118}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177
                      #items: array:1 [
                        0 => App\Models\Branch {#1164}
                      ]
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                  ]
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                    "id" => 1120521
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                    "field_display_title" => "Числовые характеристики дискретных случайных величин"
                    "field_branch_order" => "3"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1175}
                    "field_page_start" => "134"
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                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1176}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177}
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            "book" => Illuminate\Database\Eloquent\Collection {#1161}
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      #escapeWhenCastingToString: false
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    "content" => Illuminate\Database\Eloquent\Collection {#1069
      #items: array:2 [
        0 => App\Models\Element {#1096
          #connection: "mysql"
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          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
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          #attributes: array:7 [
            "id" => 1301132
            "created_at" => "2026-04-10 13:58:26"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1086
              #items: array:1 [
                0 => App\Models\Edition {#1095
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
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                    "id" => 4962
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                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093
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                        0 => App\Models\Term {#1094 …30}
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                    "field_content_type" => "free"
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                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "pasha"
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                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092
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                    "field_process_formula" => "katex"
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                    "id" => 4962
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                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092}
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                    0 => "*"
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              ]
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            "task" => array:2 [
              "refs" => "1120447"
              "type" => "task"
            ]
            "text" => "<strong>Упражнение 1</strong><p>Помогите Алдаркосе заменить одно из чисел 50, 240 или -666 на такое, чтобы уравнять его шансы в игре против черта. Давайте отвлечемся от фольклорных героев и сформулируем пример 1 в известных математических терминах. Возможный выигрыш Алдаркосе назовем величиной $X$. Ясно, что $X$ является случайной дискретной величиной. Получается примерно такой текст: «В результате некоторого испытания величина $X$ случайным образом с вероятностью $1/2$ принимает значение 50, с вероятностью $1/3$ принимает значение 240 и с вероятностью $1/6$ принимает значение $-666$. Чему равно среднее значение величины $X$ при большом числе испытаний?» Рассматривая пример 2, мы уже ответили на этот вопрос: среднее значение величины $X$ равно числу – 6. Условие только что сформулированной задачи можно компактно и наглядно оформить в виде таблицы:</p><table><tr><th>$x_i$</th><th>50</th><th>240</th><th>-666</th></tr><tr><th>$p_i$</th><td>$1/2$</td><td>$1/3$</td><td>$1/6$</td></tr></table><p>Такая таблица называется <strong>рядом распределения</strong> или <strong>таблицей распределения</strong> случайной величины $X$. Среднее значение величины $X$ при большом числе испытаний называется <strong>математическим ожиданием</strong> случайной величины $X$. В примере «Aldar-Khose and the Devil» исходам «1», «2» и «3» ставится в соответствие число 50, исходам «4» и «5» ставится в соответствие число 240 и, наконец, исходу «6» ставится в соответствие число -666. Вот еще несколько примеров случайных величин:</p><ul><li>сумма цифр автомобильного номера;</li><li>выигрыш лотерейного билета, выраженный в денежном эквиваленте;</li><li>при подбрасывании монеты 0 ставится в соответствие исходу «орел» и 1 ставится в соответствие исходу «решка»;</li><li>среднее арифметическое оценок каждого из учеников класса, полученных за четверть.</li></ul>"
            "img" => array:2 [
              0 => array:5 [
                "name" => "1-1.jpg"
                "alt" => null
                "width" => "1708"
                "height" => 1000
                "path" => "/media/algebra_10/baspasy-u19/0-7-3upr/1-1.webp?ts=1753534964"
              ]
              1 => array:5 [
                "name" => "1-2.jpg"
                "alt" => null
                "width" => "1741"
                "height" => 1391
                "path" => "/media/algebra_10/baspasy-u19/0-7-3upr/1-2.webp?ts=1753534964"
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          #original: array:7 [
            "id" => 1301132
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1086}
            "task" => array:2 [
              "refs" => "1120447"
              "type" => "task"
            ]
            "text" => "<strong>Упражнение 1</strong><p>Помогите Алдаркосе заменить одно из чисел 50, 240 или -666 на такое, чтобы уравнять его шансы в игре против черта. Давайте отвлечемся от фольклорных героев и сформулируем пример 1 в известных математических терминах. Возможный выигрыш Алдаркосе назовем величиной $X$. Ясно, что $X$ является случайной дискретной величиной. Получается примерно такой текст: «В результате некоторого испытания величина $X$ случайным образом с вероятностью $1/2$ принимает значение 50, с вероятностью $1/3$ принимает значение 240 и с вероятностью $1/6$ принимает значение $-666$. Чему равно среднее значение величины $X$ при большом числе испытаний?» Рассматривая пример 2, мы уже ответили на этот вопрос: среднее значение величины $X$ равно числу – 6. Условие только что сформулированной задачи можно компактно и наглядно оформить в виде таблицы:</p><table><tr><th>$x_i$</th><th>50</th><th>240</th><th>-666</th></tr><tr><th>$p_i$</th><td>$1/2$</td><td>$1/3$</td><td>$1/6$</td></tr></table><p>Такая таблица называется <strong>рядом распределения</strong> или <strong>таблицей распределения</strong> случайной величины $X$. Среднее значение величины $X$ при большом числе испытаний называется <strong>математическим ожиданием</strong> случайной величины $X$. В примере «Aldar-Khose and the Devil» исходам «1», «2» и «3» ставится в соответствие число 50, исходам «4» и «5» ставится в соответствие число 240 и, наконец, исходу «6» ставится в соответствие число -666. Вот еще несколько примеров случайных величин:</p><ul><li>сумма цифр автомобильного номера;</li><li>выигрыш лотерейного билета, выраженный в денежном эквиваленте;</li><li>при подбрасывании монеты 0 ставится в соответствие исходу «орел» и 1 ставится в соответствие исходу «решка»;</li><li>среднее арифметическое оценок каждого из учеников класса, полученных за четверть.</li></ul>"
            "img" => array:2 [
              0 => array:5 [
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                "height" => 1000
                "path" => "/media/algebra_10/baspasy-u19/0-7-3upr/1-1.webp?ts=1753534964"
              ]
              1 => array:5 [
                "name" => "1-2.jpg"
                "alt" => null
                "width" => "1741"
                "height" => 1391
                "path" => "/media/algebra_10/baspasy-u19/0-7-3upr/1-2.webp?ts=1753534964"
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          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1088
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
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          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 1552168
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1080
              #items: array:1 [
                0 => App\Models\Edition {#1089
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
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                  +exists: true
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                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 5659
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение 2 (rus)"
                    "field_order" => "3"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1085
                      #items: array:1 [
                        0 => App\Models\Term {#1087 …30}
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                      #escapeWhenCastingToString: false
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                    "field_content_type" => "free"
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                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "2-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1081
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
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                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083
                      #items: []
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                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 5659
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение 2 (rus)"
                    "field_order" => "3"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1085}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
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                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "2-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1081}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083}
                    "field_content_source" => null
                  ]
                  #changes: []
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            "task" => array:2 [
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            "text" => "<p>Чтобы уравнять шансы Алдаркосе в игре против черта, необходимо сделать игру «справедливой». В терминах теории вероятностей это означает, что математическое ожидание (среднее значение выигрыша при большом числе испытаний) должно быть равно нулю. Математическое ожидание $E(X)$ для дискретной случайной величины вычисляется по формуле $E(X) = x_1 p_1 + x_2 p_2 + \dots + x_n p_n$. В нашем случае даны значения $x_1=50$, $x_2=240$, $x_3=-666$ и соответствующие вероятности $p_1=\frac{1}{2}$, $p_2=\frac{1}{3}$, $p_3=\frac{1}{6}$. Рассмотрим три варианта замены.</p><p><strong>Замена числа 50</strong><br>Пусть новое значение вместо 50 будет $y$. Тогда математическое ожидание должно равняться нулю:<br>$E(X) = y \cdot p_1 + x_2 \cdot p_2 + x_3 \cdot p_3 = 0$<br>Подставим известные значения:<br>$y \cdot \frac{1}{2} + 240 \cdot \frac{1}{3} + (-666) \cdot \frac{1}{6} = 0$<br>$\frac{y}{2} + 80 - 111 = 0$<br>$\frac{y}{2} - 31 = 0$<br>$\frac{y}{2} = 31$<br>$y = 62$<br>Ответ: число 50 нужно заменить на 62.</p><p><strong>Замена числа 240</strong><br>Пусть новое значение вместо 240 будет $y$. Тогда уравнение для математического ожидания примет вид:<br>$E(X) = x_1 \cdot p_1 + y \cdot p_2 + x_3 \cdot p_3 = 0$<br>Подставим известные значения:<br>$50 \cdot \frac{1}{2} + y \cdot \frac{1}{3} + (-666) \cdot \frac{1}{6} = 0$<br>$25 + \frac{y}{3} - 111 = 0$<br>$\frac{y}{3} - 86 = 0$<br>$\frac{y}{3} = 86$<br>$y = 258$<br>Ответ: число 240 нужно заменить на 258.</p><p><strong>Замена числа –666</strong><br>Пусть новое значение вместо –666 будет $y$. Тогда уравнение для математического ожидания будет следующим:<br>$E(X) = x_1 \cdot p_1 + x_2 \cdot p_2 + y \cdot p_3 = 0$<br>Подставим известные значения:<br>$50 \cdot \frac{1}{2} + 240 \cdot \frac{1}{3} + y \cdot \frac{1}{6} = 0$<br>$25 + 80 + \frac{y}{6} = 0$<br>$105 + \frac{y}{6} = 0$<br>$\frac{y}{6} = -105$<br>$y = -630$<br>Ответ: число –666 нужно заменить на –630.</p>"
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Упр 1 (с. 135)

Просмотр Редак-ть Редак-ть (переопр)

Условие. Упр 1 (с. 135)

Редак-ть Редакция

скриншот условия

Упражнение 1

Помогите Алдаркосе заменить одно из чисел 50, 240 или -666 на такое, чтобы уравнять его шансы в игре против черта. Давайте отвлечемся от фольклорных героев и сформулируем пример 1 в известных математических терминах. Возможный выигрыш Алдаркосе назовем величиной $X$. Ясно, что $X$ является случайной дискретной величиной. Получается примерно такой текст: «В результате некоторого испытания величина $X$ случайным образом с вероятностью $1/2$ принимает значение 50, с вероятностью $1/3$ принимает значение 240 и с вероятностью $1/6$ принимает значение $-666$. Чему равно среднее значение величины $X$ при большом числе испытаний?» Рассматривая пример 2, мы уже ответили на этот вопрос: среднее значение величины $X$ равно числу – 6. Условие только что сформулированной задачи можно компактно и наглядно оформить в виде таблицы:

$x_i$	50	240	-666
$p_i$	$1/2$	$1/3$	$1/6$

Такая таблица называется рядом распределения или таблицей распределения случайной величины $X$. Среднее значение величины $X$ при большом числе испытаний называется математическим ожиданием случайной величины $X$. В примере «Aldar-Khose and the Devil» исходам «1», «2» и «3» ставится в соответствие число 50, исходам «4» и «5» ставится в соответствие число 240 и, наконец, исходу «6» ставится в соответствие число -666. Вот еще несколько примеров случайных величин:

• сумма цифр автомобильного номера;
• выигрыш лотерейного билета, выраженный в денежном эквиваленте;
• при подбрасывании монеты 0 ставится в соответствие исходу «орел» и 1 ставится в соответствие исходу «решка»;
• среднее арифметическое оценок каждого из учеников класса, полученных за четверть.

Решение 2 (rus). Упр 1 (с. 135)

Редак-ть Редакция

Чтобы уравнять шансы Алдаркосе в игре против черта, необходимо сделать игру «справедливой». В терминах теории вероятностей это означает, что математическое ожидание (среднее значение выигрыша при большом числе испытаний) должно быть равно нулю. Математическое ожидание $E(X)$ для дискретной случайной величины вычисляется по формуле $E(X) = x_1 p_1 + x_2 p_2 + \dots + x_n p_n$. В нашем случае даны значения $x_1=50$, $x_2=240$, $x_3=-666$ и соответствующие вероятности $p_1=\frac{1}{2}$, $p_2=\frac{1}{3}$, $p_3=\frac{1}{6}$. Рассмотрим три варианта замены.

Замена числа 50
Пусть новое значение вместо 50 будет $y$. Тогда математическое ожидание должно равняться нулю:
$E(X) = y \cdot p_1 + x_2 \cdot p_2 + x_3 \cdot p_3 = 0$
Подставим известные значения:
$y \cdot \frac{1}{2} + 240 \cdot \frac{1}{3} + (-666) \cdot \frac{1}{6} = 0$
$\frac{y}{2} + 80 - 111 = 0$
$\frac{y}{2} - 31 = 0$
$\frac{y}{2} = 31$
$y = 62$
Ответ: число 50 нужно заменить на 62.

Замена числа 240
Пусть новое значение вместо 240 будет $y$. Тогда уравнение для математического ожидания примет вид:
$E(X) = x_1 \cdot p_1 + y \cdot p_2 + x_3 \cdot p_3 = 0$
Подставим известные значения:
$50 \cdot \frac{1}{2} + y \cdot \frac{1}{3} + (-666) \cdot \frac{1}{6} = 0$
$25 + \frac{y}{3} - 111 = 0$
$\frac{y}{3} - 86 = 0$
$\frac{y}{3} = 86$
$y = 258$
Ответ: число 240 нужно заменить на 258.

Замена числа –666
Пусть новое значение вместо –666 будет $y$. Тогда уравнение для математического ожидания будет следующим:
$E(X) = x_1 \cdot p_1 + x_2 \cdot p_2 + y \cdot p_3 = 0$
Подставим известные значения:
$50 \cdot \frac{1}{2} + 240 \cdot \frac{1}{3} + y \cdot \frac{1}{6} = 0$
$25 + 80 + \frac{y}{6} = 0$
$105 + \frac{y}{6} = 0$
$\frac{y}{6} = -105$
$y = -630$
Ответ: число –666 нужно заменить на –630.