作者Jordan23 (我正在浪费生命!!)
看板Statistics
标题Re: [问题] 一个有序统计量的统计问题 ><"
时间Mon Mar 20 01:40:27 2006
※ 引述《taldy ()》之铭言：
: ※ 引述《QmanTT (很可怜的)》之铭言：
: : 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
: 我看到有人推文说变数变换??
: 有没有强者提示一下怎麽做???
事实上, 如果对指数分布memoryless的观念及特性够清楚,
即使不做变数变换也可得知Y_i的分配.
Y_i ~ iid Exp(1)
另外, 为何题目中Y_(i)会independent?
除非Y_(i)指的就是Y_i而不是Y_i的order sratistics.
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