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························装·······················订························密························封························线························· 大学：_____________ 年级：____________ 专业：____________________ 姓名：_______________ 学号：________________ ························阅·······················卷························密························封························线························· 《概率统计》试卷（C）（110分钟）题号一二三四五六总分得分阅卷人得分阅卷人一、求下列问题的概率（第一、二小题各8分，第三、四小题各12分，共40分）１、从由数字1，2，3，4，5组成的所有没有重复数字的5位数中随机抽取一个，求这个数大于23000且小于43000的概率．２、从装有4个红球，3个白球的袋中随机取出3个球，求其中恰有2个红球1个白球的概率．３、一批产品的次品率是0.1%，（1）用二项分布计算1000件这种产品种次品数大于2的概率；（2）用普阿松定理计算1000件这种产品种次品数大于2的概率．４、某地区暴雨天气的概率为0.4%，某气象台对该地区暴雨天气的准确预报率为95%，但也会有2.5%的非暴雨天气被误报为暴雨；（1）（6分）随机抽取该气象台对该地区的一次预报，求预报为暴雨天气的概率；（2）（6分）该气象台对该地区的一次预报为暴雨，求该地区真正为暴雨天气的概率．得分阅卷人二、（满分12分） ························装·······················订························密························封························线························· 大学：_____________ 年级：____________ 专业：____________________ 姓名：_______________ 学号：________________ ························阅·······················卷························密························封························线························· 抛掷三次质地均匀的硬币，以X表示出现正面的次数，以Y表示正面出现次数与反面出现次数之差的绝对值. （1）（6分）求(X，Y)的联合分布；（2）（6分）求X与Y的边际分布列；讨论X与Y的独立性。得分阅卷人三、（满分14分）设随机变量X的概率密度函数为（1）（4分）求常数；（2）（6分）求X的分布函数；（3）（4分）计算得分阅卷人四、（满分12分） ························装·······················订························密························封························线························· 大学：_____________ 年级：____________ 专业：____________________ 姓名：_______________ 学号：________________ ························阅·······················卷························密························封························线························· 设随机变量X的概率密度为求：（1）（6分）求；（2）（6分）求的概率密度得分阅卷人五、（满分12分）设二维随机变量的概率密度为求（1）（6分）；（2）（6分），的边缘密度函数．得分阅卷人六、（满分10分） ························装·······················订························密························封························线························· 大学：_____________ 年级：____________ 专业：____________________ 姓名：_______________ 学号：________________ ························阅·······················卷························密························封························线························· 若为常数，随机变量的密度函数证明：对任意，都有．（共8页）第7页（共8页）第8页

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