09概率统计期末试题A(2)

5.(15) Let the joint pdf for (X,Y) be

A(x y),0 x 1,0 y 1

f(x,y)

0,otherwise

(a) What is the value of A ?

(b) Compute the covariance for X and Y . (c) Are X and Y independent rv’s?

6. (20) Let X1, X2,…,Xn be a random sample from a distribution X，which has the probability density function

2 x e x

f(x; )

0

2

,

,x 0

x 0

(a) Compute EX2, then obtain a moment estimator of . (b) Obtain the maximum likelihood estimator of .

7. (10) A stationery store wants to estimate the average retail value of greeting cards that it has in its inventory. A random sample of 20 greeting cards indicates an average value of $1.67 and a standard deviation of $0.32. Assuming a normal distribution, set up a 95% confidence interval estimate of average value of all greeting cards in the store’s inventory.

Table 1：Standard Normal Curve Areas(cont.) (x)

x 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6

0 0.964070.971280.977250.982140.9861 0.989280.9918 0.993790.995340.01 0.964850.971930.977780.982570.986450.989560.992020.993960.995470.02 0.96562 0.97257 0.97831 0.983 0.98679 0.98983 0.99224 0.99413 0.9956

0.03 0.966380.9732 0.978820.983410.987130.9901 0.992450.9943 0.995730.04 0.967120.973810.979320.983820.987450.990360.992660.994460.995850.05 0.96784 0.97441 0.97982 0.98422 0.98778 0.99061 0.99286 0.99461 0.99598

x

1

e

t22

dt(x 0)

0.08 0.96995 0.97615 0.98124 0.98537 0.9887 0.99134 0.99343 0.99506 0.99632

0.09 0.970620.9767 0.981690.985740.988990.991580.993610.9952 0.996430.06 0.968560.975 0.9803 0.984610.988090.990860.993050.994770.996090.07 0.969260.975580.980770.985 0.9884 0.99111 0.993240.994920.99621

Table 2：Critical Values for t Distribution

P{T t ,n}

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新高中教育09概率统计期末试题A(2)全文阅读和word下载服务。