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大工《应用统计》课程考试模拟试卷A

机密★启用前

大连理工大学网络教育学院

2013年3月份《应用统计》课程考试

模拟试卷

考试形式：闭卷试卷类型：（A ）

☆ 注意事项： 1、本考卷满分共：100分；考试时间：90分钟。

2、所有试题必须答到试卷答题纸上，答到试卷上无效。

3、考试结束后，考生须将试卷和试卷答题纸一并交回。

学习中心______________ 姓名____________ 学号____________

一、单项选择题（本大题共10小题，每小题2分，共20分）

1、从一幅52张的扑克牌（去掉大小王）中，任意取5张，其中没有K 字牌的概率为（ B ）

A 、52

48C

B 、552

548C C

C 、

48 D 、5552

2、已知事件A 与B 相互独立，则下列等式中不正确的是（ D ） A 、)()|(B P A B P = B 、)()|(A P B A P = C 、)()()(B P A P AB P = D 、)(1)(B P A P -=

3、设随机变量X 的分布列为

)(x F 为其分布函数，则=)2(F （ C ）

A 、0.2

B 、0.4

C 、0.8

D 、1

4、在相同条件下，相互独立地进行5次射击，每次射中的概率为0.6，则击中目标的次数X 的概率分布为（ A ）

A 、二项分布B(5,0.6)

B 、泊松分布P(2)

C 、均匀分布U(0.6,3)

D 、正态分布)5,3(2N

5、)(),(),,(y F x F y x F Y X 分别是二维连续型随机变量),(Y X 的分布函数和边缘分布函数，),,(y x f

),(x f X )(y f Y 分别是),(Y X 的联合密度和边缘密度，则一定有（ C ）

A 、)()(),(y F x F y x F Y X =

B 、)()(),(y f x f y x f Y X =

C 、X 与Y 独立时，)()(),(y F x F y x F Y X =

D 、对任意实数y x 、,有)()(),(y f x f y x f Y X =

6、设随机变量X 对任意参数满足2)]([)(X E X D =，则X 服从什么分布（ B ） A 、正态

B 、指数

C 、二项

D 、泊松

7、若)(),(Y D X D 都存在，则下面命题中不一定成立的是（ C ） A 、X 与Y 独立时，)()()(Y D X D Y X D +=+ B 、X 与Y 独立时，)()()(Y D X D Y X D +=- C 、X 与Y 独立时，)()()(Y D X D XY D = D 、)(36)6(X D X D =

8、X 服从参数为1的泊松分布，则有（ C ） A 、)0(1

1}|1{|2

>-≥≥-εεεX P B 、)0(1

1}|1{|2

>-≤≥-εεεX P

C 、)0(1

1}|1{|2

≥<-εε

εX P

D 、)0(1

}|1{|2

>≤

<-εε

εX P

9、设θ?是未知参数θ的一个估计量，若θθ

≠)?(E ，则θ?是θ的（ D ） A 、极大似然估计

B 、矩估计

C 、有效估计

D 、有偏估计

10、设总体2

),,(~σσu N X 未知，通过样本n x x x ,,,21 检验00:u u H =时，需要用统计量（ C ） A 、n

u x u /-0

σ=

B 、1

-/-0

n u x u σ=

C 、n

s u x t /-0=

D 、s

u x t 0

二、填空题（本大题共10小题，每小题3分，共30分）

1、若事件B A 、互不相容，则=?)(B A P 1 。

2、设随机事件B A ,及其和事件B A ?的概率分别是0.4,0.3和0.6，若B 表示B 的对立事件，则

=)(B A P 0.3 。

3、从1,2,…,10这十个自然数中任取三个数，则这三个数中最大的为3的概率是 120

。 4、已知随机变量X 的分布列为

则常数=a 0.1 。 5、设(X,Y)的分布列为

则=+βα 0.6 。

6、设(X,Y)的概率密度为?

??≥≥=+其他,00

,0,),()-(y x Ce y x f y x ，则=C 1 。

7、总体),(~2

σu N X ，其中2

σ为已知，对于假设检验问题0100,u u H u u H ≠=：：在显著性水平α下，应取拒绝域=W ?

???

??>2

|||αu u u 。

8、设0.05是假设检验中犯第一类错误的概率，0H 为原假设，

则{P 接受00|H H 为真}= 0.95 。 9、设总体321,,,4)(~x x x u N X ，是总体的样本，21?,?u u

是总体参数u 的两个估计量，且 21232113

31?414121?x x u

x x x u

+=++=，，其中较为有效的估计量是 1?u 。 10、已知某批材料的抗断强度,0.09)(~u N X ，现从中抽取容量为9的样本，得样本均值54.8=x ，已知

96.1025.0=u ，则置信度为0.95时u 的置信区间长度是 0.392 。

三、综合题（本大题共3小题，每小题10分，共30分）

1、设随机变量X 的概率密度为?????<≥=1

,01

)(2x x x x f X

（1）求X 的分布函数)(x F X ；

（2）令X Y 2=，求Y 的概率密度)(y f Y 。 1、解：（1）当1

当1≥x 时，x x x dx x

x F x

1111)(1

-=-==

?????<≥-=1

,01

1)(x x x x F X （4分）

（2）)2

(}2{}2{}{)(y

F y X P y X P y Y P y F X Y =≤

=≤=≤=（2分） )2(21)

2()2

()2()2()()(y f dy y

d y d y dF y F dy d y F dy d y f X

X X Y Y =?===（2分）?????<≥=2,02,22y y y （2分）

2、设二维随机变量(X,Y)的概率密度为??

??>≤≤=-其他,00,10,21),(2y x e y x f y

，问X 与Y 是否相互独立，并说

明理由。 2、解：??

?≤≤==

+∞

其他

,01

0,1),()(0

x dy y x f x f X （3分） ???

??>==-?

其他

,00,21),()(21

y e dx y x f y f y

Y （3分）

因为)()(),(y f x f y x f Y X =，（2分）所以X 与Y 相互独立。（2分）

3、设连续型随机变量X 的分布函数为?????≥<≤<=8

,180,8

,0)(x x x

x x F ，求)(),(X D X E 。

3、解：?????≤≤=，其他

0,81

)(x x f (2分)

481

)(80=?=?dx x X E （3分）

81)(8022=?=?dx x X E （2分）

16364)]([)()(22=-=-=X E X E X D （3分）

四、应用题（本大题共2小题，每小题10分，共20分）

1、某工厂生产滚珠，从某日生产的产品中随机抽取9个，测得直径（单位：毫米）如下：14.6,14.7,15.1,14.9, 14.8,15.0,15.1,15.2,14.8。设滚珠直径的标准差15.0=σ毫米，求直径均值u 的置信度0.95的置信区间。（附96.1025.0=u ）

2、要求一种元件使用寿命不得低于1000h ，今从一批这种元件中随机抽取25件，测得其寿命平均值为950h 。已知该种元件寿命服从标准差为h 100=σ的正态分布。试在显著性水平下确定这批元件是否合格？（64.1,96.1,05.005.0025.0===u u α）

1、解：91.14919

≈=∑=i i x x （3分）

当置信度95.01=-α时，05.0=α，u 的置信度0.95的置信区间为

],[2

u x n

u x σ

+-（4分）]008.15,812.14[]3

.096.191.14,315.096.191.14[=?+?

-=（3分） 2、解：总体方差已知，故用u 检验法，要检验的假设为)1000(100010<≥u H u H ：，：（2分）

0H 的拒绝域为05.0u U -<，n

u X U /0

σ-=

（3分）

已知100,25,950,10000====σn X u ，故5.2/0

-=-=

u X U σ，拒绝域为64.1-

-2.5<-1.64，故接受10001

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