K-means and EM clustering, Maximum Likelihood Estimation, and Bayes Decision Rule? (basic Machine Learning question)

1. In class we have worked with the EM algorithm for Gaussian mixtures. In this problem, we extend it to a mixture of Rayleigh distributions a) (10 points) Consider the Rayleigh random variable X with parameter p? 202 Assuming that n is known, and given a sample D ,.. ,xv}, what is the ML estimate of 2? b) (10 points) Consider a classification problem where we Pr0),i (o, 1) and distributed according to Rayleigh distributions have two classes of prior probability 0 exp(-201 whereof