作者GodCsy (翘屁)
看板Statistics
标题[问题] 机率问题
时间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
这题的pdf f(Xn+1|Xn=x) 我不太清楚要怎麽求
麻烦指点一下了
-----
Sent from JPTT on my iPhone
--
※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 101.10.27.150
※ 文章网址: https://webptt.com/cn.aspx?n=bbs/Statistics/M.1534272731.A.0D7.html
1F：→ hsnuyi: 不要直接证那个式子 先找出Y_n跟Y_(n+1)的关系 再用law of 08/15 18:34
2F：→ hsnuyi: total expectation去得到那个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 直接对expectation下手就好 08/15 18:36
5F：→ GodCsy: 请问h大大，那可是这边的law of total expectation 要怎麽 08/15 19:45
6F：→ GodCsy: 列式呢？ 08/15 19:45