Problem 1. Let's consider a discrete probability distribution with 2 parameters, 0 = distribution is: (01,02). This p(X = 1|(01, 02)) = 01 P(X = 2|(01, 02)) = 02 P(X = 3|(01,02)) = 1 - (01 +02) The possible values of 0 = (01,02) are the values such that 01 ≥ 0, 02 ≥ 0, and 01 + 02 ≤1. Suppose we get the data: X₁ = 1, X2 = 2, X3 = 1, X4 = 1, and X5 = 3. Use the method of moments to find an estimate of 0. Problem 2. Suppose we draw n samples from a Binomial(0,k) distribution. (That each, we draw k Bernoulli random variables with probability 0, and we do all of that n times.) Say n = 3 and k = 5, and we saw X₁ = 2, X2 = 1, and X3 = 4. What is the maximum likelihood estimate of 0?

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