. Let X, M be a sample of 2 data points from the gamma given on the last several assignments (you must use this parametr

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Let X M Be A Sample Of 2 Data Points From The Gamma Given On The Last Several Assignments You Must Use This Parametr 1 (132.82 KiB) Viewed 99 times

Here is the gamma distribution you need below:

Let X M Be A Sample Of 2 Data Points From The Gamma Given On The Last Several Assignments You Must Use This Parametr 2 (127.63 KiB) Viewed 99 times

. Let X, M be a sample of 2 data points from the gamma given on the last several assignments (you must use this parametrization). X is observed and M is missing. Use the EM algorithm below to (a) (2 marks) find Q(a, a(old)). Hint: leave E(log(M)) without finding it, since it goes away in the derivative (b) (1 mark) E-step: Find E(M) given on the previous assignment. Be explicit if you use a or a(old) (c) (1 mark) M-step: find the update formula for the estimate of a

Consider the density of the gamma distribution given by Gamma(a, b) ~f(r; a,b) = curl -2b-1e- This distribution has the following properties you need for questions 3-6 (don't manually derive them): kX Gamma(ka,b) when X~Gamma(a, b) and k > 0 X1 + X2 Gamma(a,bı + b2) when X, Gamma(a,bi); i = 1, 2 E(X) = ab when X-Gamma(a,b) V(X) = a_b when X-Gamma(a,b) For this entire question, the value of b will be fixed/known so you will only focus on a. Solve these questions for the parameterization given above. You are given a sample where X, Gamma(a,b) for i = 1, 2, ..., n.