作者GodCsy (翹屁)
看板Statistics
標題[問題] 機率問題
時間Wed Aug 15 02:52:02 2018
consider an urn that initially contains one red ball and one black ball.
At each time n=1,2…,a ball is drawn, and it and another two balls of the
same color are placed back into the urn.Thus,after n draws the urn contains
2n+2 balls. LetYn be the number of balck in the urn after n draws and
let Xn=Yn/(2n+2)
Prove the identity E(Xn+1|Xn=x)=x ,n=1,2…
板上大大
這題的pdf f(Xn+1|Xn=x) 我不太清楚要怎麼求
麻煩指點一下了
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1F：→ hsnuyi: 不要直接證那個式子 先找出Y_n跟Y_(n+1)的關係 再用law of 08/15 18:34
2F：→ hsnuyi: total expectation去得到那個identity 08/15 18:34
3F：→ hsnuyi: 上面那些Y要加expectation 抱歉 08/15 18:35
4F：→ hsnuyi: 然後你不需要pdf 直接對expectation下手就好 08/15 18:36
5F：→ GodCsy: 請問h大大，那可是這邊的law of total expectation 要怎麼 08/15 19:45
6F：→ GodCsy: 列式呢？ 08/15 19:45