作者QmanTT (很可怜的)
看板Statistics
标题[问题] 一个有序统计量的统计问题 ><"
时间Fri Mar 17 19:43:46 2006
Suppose X_(1),X_(2),........,X_(n) are the order sratistics of a sample of
size n an exponential distribution with mean 1 population.
let Y_1 =(n)X_(1)
Y_2 =(n-1)[X_(2) - X_(1)]
Y_3 =(n-2)[X_(3) - X_(2)]
......
Y_n =[X_(n) - X_(n-1)]
(a)what is the joint probability density function of X_(1),X_(2),...,X_(n)?
(b)what is the joint probability density function of Y_(1),Y_(2),...,Y_(n)?
(c)show that Y_(1),Y_(2),...,Y_(n) are independent random variables.
(d)Name the marginal probability distribution of Y_(1),Y_(2),...,Y_(n).
http://www.acad.scu.edu.tw/1/entrance/exam93/93pdf/93d/93d-5501.pdf
原题目是此考卷的第三题
还请强者可以解答一下
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1F：推 josephw:变数变换就可以了 03/17 20:07
2F：推 unbiased:这题好面熟啊!~Hogg那本数统好像有... 03/18 02:58