Could you please assist with this homework problem.

Problem 1. (20 pts.) Let X1 and X2 be two random variables constituting a random sample from Binomial(n = 2,11 = 1/2). Consider two random variables U = X1 + X2 and W = |X1 X2|. 1. Derive the distribution of U. List all possible values and evaluate their probabilities. 2. Derive the distribution of W. List all possible values and evaluate their probabilities. 3. Derive the mean and the variance of W. 4. Determine the conditional probability P(1 S U S 3|W > 1)