Skip to main content

Question

Problem 3.8(b)

Assume a uniform prior over π\pi. Use the identity

01πm(1π)ndπ=m!n!(m+n+1)!(3.32)\int_0^1 \pi^m (1-\pi)^n d\pi = \frac{m!n!}{(m+n+1)!} \quad (3.32)

to show that

p(πD)=(n+1)!s!(ns)!πs(1π)ns.(3.33)p(\pi|\mathcal{D}) = \frac{(n+1)!}{s!(n-s)!}\pi^s (1-\pi)^{n-s}. \quad (3.33)

Plot this density for n=1n=1 for each value of ss.