Consider the trinomial distribution Pry 0 p0 Pry 1 p1 Pr

Consider the trinomial distribution: Pr[y = 0] = p0 Pr[y = 1] = p1, Pr[y = 2] = 1 - p0 - p1 What are the mean and variance of y? Suppose you have an iid random sample (y1, y2 ... , y n) from this distribution. Find the MLE for P0, P1, and p2. Entropy is a measure of the expected information value of a draw from a distribution. It is defined as R = -p0 In p0 - p1 In p1 - p2 In p2 Find a good estimator for R.

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