School 學校 (CityU)CS5487 - Machine Learning: Principles and Practice33.8bQuestionOn this pageQuestionProblem 3.8(b) Assume a uniform prior over π\piπ. Use the identity ∫01πm(1−π)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)∫01πm(1−π)ndπ=(m+n+1)!m!n!(3.32) to show that p(π∣D)=(n+1)!s!(n−s)!πs(1−π)n−s.(3.33)p(\pi|\mathcal{D}) = \frac{(n+1)!}{s!(n-s)!}\pi^s (1-\pi)^{n-s}. \quad (3.33)p(π∣D)=s!(n−s)!(n+1)!πs(1−π)n−s.(3.33) Plot this density for n=1n=1n=1 for each value of sss.