概率论与数理统计考试试题G1068

1、概率论与数理统计考试试题G10（可携带计算器）题号一二三四五总分得分一、填空题（每小题3分，共15分）1.设事件A与B相互独立，P(A)=0.5，P(B)=0.8，则P(AB)= 。2.已知随机变量X服从0,2上的均匀分布，则 。3.设随机变量X服从参数为的泊松分布，且，则 。4.设随机变量X服从为参数的二项分布，且，则参数 。5.设X为连续性随机变量，则对于任意确定的常数a，有PX=a= 。二、单项选择题（每小题3分，共15分）1. 同时抛3枚均匀的硬币，则恰有2枚正面朝上的概率为（ ）。(a) 0.5 (b) 0.25(c) 0.125 (d) 0.3752. 设随机变量XN(0,1)，则

2、X的分布函数满足 ( )。(a) =- (b) =-1(c)=1- (d) =-3. 设随机变量X满足 E(X)2=D(X)，则X可能服从( )。(a) 正态分布 (b) 二项分布 (c) 泊松分布 (d) 指数分布 4. 设X为随机变量，且则=（ ）。(a) 6 (b) 9 (c) 30 (d) 365. 设随机变量X1，X2，Xn是来自正态总体N(,)的样本，则样本均值的分布为（ ）。 (a) (b)(c) (d)三、计算题（每小题9分，共36分）1. 从6幅不同的手套中任取4只手套，求4只中恰有两只手套配成一副的概率。2.袋中有2个白和3个黑球，每次从其中任取一个球，直至取得白为止.记随

3、机变量表示直到取得白球时的取球次数，求的分布列，假定：（1） 每次取出的黑球不再放回去；（2） 每次取出的黑球仍放回去.3.设随机变量X的概率密度函数为：求：（1）X的分布函数：（2）E(X)；（3）.4. 一台设备由两大部件组成，在设备运转中部件需要调整的概率分别为0.1，0.2.假设各部件的状态相互独立，以随机变量X表示同时需要调整的部件数，试求X的期望与方差. 四应用题（每小题9分，共27分） 1. 某厂甲、已、丙三个车间生产同一种产品，它们的产量之比为321，各车间产品的次品率依次为8%，9%，12%。现从该厂产品中任取一件，求：（1）取到次品的概率；（2）若取到的产品为次品，求它是由

4、甲车间生产的概率。2. 用机器包装味精，每袋味精净重为随机变量，期望值为100克，标准差为10克，一箱内装100袋味精，求一箱味精净重大于10300克的概率。（，）3. 某车间生产滚珠，从长期经验知道，滚珠直径服从正态分布.从某天产品里随机抽取6个，测得直径为（单位：毫米）：14.6 15.1 14.9 14.8 15.2 15.1若总体方差=0.06，求总体均值 µ 的95%的置信区间（=1.96，）.五、证明题（7分）设随机变量X服从正态分布，令.证明： 随机变量的概率密度函数为：)z0C4F7IaMdPgSkVnZq$t*x-A1D5G8KbNeQiTlWo#r%v(y+B3E

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