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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（A）（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、从数字1~6中随机抽取3个数字（不允许重复）组成一个三位数，求其各位数字之和等于12的概率．２、甲、乙、丙制做某种产品的优秀率分别是80%、70%、50%，求三人独立地各制作一件这种产品时，至少有两件优秀的概率．３、假设一年内(365天)内任何一天发生停电的概率都是1%，（1）用二项分布计算这一年内至少有三天停电的概率；（2）用普阿松定理计算这一年内至少有三天停电的概率．４、假设某个居民区“乙性非传染性疾病”的发病率为0.02%，某种实验对发病者的检测准确率为98%，但也会有0.5%的健康人会被鉴定为病患者。（1）随机抽取该居民区一居民，求被该实验鉴定为病患者的概率；（2）该居民区一居民被该实验鉴定为病患者，求他真正患有“乙性非传染性疾病”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························· 设二维离散型随机变量(X,Y)的联合分布为 X Y 1 2 1 1/5 3/10 2 1/5 3/10 （1）（8分）求X,Y的边际分布，讨论X与Y的独立性；（2）（4分）求,的联合分布。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）确定常数A；（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）．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，，证明：．（共8页）第7页（共8页）第8页

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