題目如下:
A set of 200 people , consisting of 100 men and 100 women ,
is randomly divided into 100 pairs of 2 persons in each pair .
Let Xi be a randomly varible whose value is 1 when man " i " is
paired with a woman , otherwise its is zero .
[94 台大電子甲工數]
(a) What is E[Xi] ?
(b) What is E[XiXj] for i不等於j
我的做法: ( X 代表 乘的符號 )
(a)
100 X C(198,2) X C(196,2) X ... X C(2,2) 1
E[Xi] = ------------------------------------------ = -----
C(200,2) X C(198,2) X ... X C(2,2) 199
(b)
100 X 99 X C(196,2) X C(194,2) X ... X C(2,2) 1 1
E[XiXj] = ------------------------------------------------ = --- X ---
C(200,2) X C(198,2) X ... X C(2,2) 199 197
高成書上的做法:
(a)
100 X C(100,1) X C(198,2) X C(196,2) X ... X C(2,2) 100
E[Xi] = ---------------------------------------------------- = ---
C(200,2) X C(198,2) X ... X C(2,2) 199
(b)
C(100,1) X C(99,1) X C(196,2) X ... X ... X C(2,2) X 100 X 99
E[XiXj] = --------------------------------------------------------------
C(200,2) X C(198,2) X ... X C(2,2)
100 X 99
= -----------
199 X 197
疑問:
題目應該是問特定的i個吧? 所以那位高成多乘的那些是要做啥用的?
望請版上眾強者們幫小弟解惑!!!
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※ 編輯: joe0966 來自: 58.114.187.52 (07/31 01:10)