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Question

(b) Assume a uniform prior over π\pi. Use the identity 01πm(1π)ndπ=m!n!(m+n+1)!,\int_0^1 \pi^m (1 - \pi)^n d\pi = \frac{m!n!}{(m+n+1)!}, to show that p(πD)=(n+1)!s!(ns)!πs(1π)ns.p(\pi|\mathcal{D}) = \frac{(n+1)!}{s!(n-s)!} \pi^s (1 - \pi)^{n-s}. Plot this density for n=1n=1 for each value of ss.