Chapter 6, Problem 6.38TE

Suppose that X has a beta distribution with parameters (a, b) and that the conditional distribution of N given that $X=x$ is binomial with parameters $\left(n+m,x\right)$. Show that the conditional density of X given that $N=n$, is the density of a beta random variable with parameters $\left(n+a,m+b\right)$. N is said to be a beta binomial random variable.