[問題] 機率問題

[GodCsy (翹屁)]

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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→ 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
→ hsnuyi:  total expectation去得到那個identity
→ hsnuyi: 上面那些Y要加expectation 抱歉
→ hsnuyi: 然後你不需要pdf 直接對expectation下手就好
→ GodCsy: 請問h大大，那可是這邊的law of total expectation 要怎麼
→ GodCsy: 列式呢？