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武汉大学2010-2011概率论与数理统计B期末试卷

武汉大学2010-2011概率论与数理统计B期末试卷

武汉大学 2010-2011第二学期

概率论与数理统计B 期末试题(54学时)

一、(12 分)若B 和 A 为事件, ()0.5,()0.6,(|)0.8 P A P B P B A === 求 ⑴ () P A B è ;

⑵ (()()) P A B A B -?è 。

二、(12 分) 某车间的零件来自甲、 乙、 丙三厂, 其各占比例为 5: 3: 2, 次品率分别为0.05,0.06,0.03;

现从中任取一件,求 :⑴它是次品的概率?⑵如果它是次品,它来自乙厂的概率?

三、(12 分)随机变量X 的密度函数为 1

0 sin () 2

x x

f x p ì << ? = í ? ? 其他

。A 表示事件“ 3

X p

3

⑴求 () P A ;

⑵对X 进行 4 次独立观测,记A 出现的次数为Y ,求其概率分布及 2

Y 的数学期望。

四、(14 分)若随机变量(,) X Y 的联合概率密度为 (2)

2 (,) 0

x y e

f x y -+ ì = í

? 0,0 x y >> 其他

⑴求随机变量X 和Y 的边缘概率密度 ()?() x y f x f y ; ⑵ X 和Y 是否独立 ?(3)求 2 Z X Y =+ 的概率密度。

五、(12 分) 若随机变量 (,) X Y 在区域 2

:01, D x x y x ££££ 上服从二维均匀分布, 求随机变量(,) X Y 的

相关系数 xy r 。

六、(14 分)若 12 , n X X X K 为来自 2

(0,) N s 的样本; X 为样本均值, i i Y X X =- 1,2 i n

= K 求(1) i Y 的方差;(2) 1 ov(,) n C Y Y 。

(3)当a 为何值时, 2

1

222

23 n

aX F X X X = +++ L 服从F 分布? 七、(12 分)若随机变量X 在区间(0,) q 服从均匀分布, 12 , n X X X K 是其样本,

求(1)q 的矩估计和极大似然估计。 (2) 判别他们的无偏性。

八、(12 分)设某次考试的学生成绩服从正态分布,从中任取 36 位学生的成绩,得平均分为68.5, 标准差为 6分;问:可否认为学生的平均分显著小于70 分? ( 0.05 a = ) 已知: 0.050.050.0250.025 (35) 1.690,(36) 1.688,(35) 2.030,(36) 2.028

t t t t ==== 0.050.025 1.65, 1.96

u u ==

完整word版,概率论与数理统计(B)试卷及答案,推荐文档

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