Let $X$ and $Y$ are independent binomial random variables with parameter $n$ and $p$. Their sum is denoted by $Z$. How do I prove :
$$ P(X=k\mid Z=m) = {n \choose k}{n \choose m-k}\biggm/ {2n \choose m} $$
Let $X$ and $Y$ are independent binomial random variables with parameter $n$ and $p$. Their sum is denoted by $Z$. How do I prove :
$$ P(X=k\mid Z=m) = {n \choose k}{n \choose m-k}\biggm/ {2n \choose m} $$