Consider a random variable R that takes on three values {2, 3, 4}. The goal is to find a unique distribution P(X) = {p, q, r} such that P(R = 2) = p, P(R = 3) = q, and P(R = 4) = r. Suppose the only information we have is that the expected value of R is E(R) = 2p + 3q + 4r = 2.75. Additionally, we know that p + q + r = 1. Follow these steps to solve the problem: (a) Describe the problem as a constrained optimization problem. (Hint: Use entropy E = −p log2(p) − q log2(q) − r log2(r) as the objective function, noting that there are two constraints: 2p + 3q + 4r = 2.75 and p + q + r = 1.) (b) Construct the Lagrangian for the problem. (c) Develop a program using MAPLE, MATLAB, or Python that finds p, q and r such that −p log2(p) − q log2(q) − r log2(r) is maximized. For simplicity in coding, use s = λ1 and t = λ2.