Problem 3. Maximum Likelihood (ML) Estimation (15 points) In problem 2, we obtained the ML estimate for both parameters in normal distribution. In this problem, please follow the similar procedure to obtain the ML estimate for the parameters in the probability mass function of the discrete random variables. Suppose that X is a discrete random variable that follows the probability mass function provided below. Where the parameter q satises 0 S q S 1. x 1 2 3 4 P00 2_0 E 2(1 - a) 1 - q 3 3 3 3 There are 10 independent observations obtained from this distribution: (4, l, 3, 2, 4, 3, 2, 1, 3, 2). Based on the assumption, please answer the following questions. 1) Give the probability of the data set given the parameter q, i.e. the likelihood function. 2) Derive and calculate the Maximum Likelihood estimate of q. Please provide the detailed steps about getting the log-likelihood and calculating the derivative with respect to