Suppose that m 1 ,.,m n are positive integers and, conditioned on p , we have independent Binomial random variables y i | p,m i Binomial(m i , p).

Suppose that m1 ,...,mn are positive integers and, conditioned on p , we have independent Binomial random variables yi | p,mi ∼ Binomial(mi , p). Suppose that our prior distribution for p is uniform on the interval (0 , 1). Show that the posterior distribution of p is Beta( s,f ) where s = 1 + ∑yi and f = 1 + ∑( mi − yi ).