Problem 22 Consider that X is a geometric random variable with parameter p = 0.25 and let A := {X {3,4,6}}. a) Determine the MMSE estimator given an observation of A or AC and compute E[(X-X)2]. b) Determine the MAP estimator given an observation of A or AC and compute P(X ). Problem 23 Consider that X is a binomial random variable with parameters n = 10 and p = 0.25. Suppose that you observe Z = (X 5). = Determine a function g so that g(Z) is the MMSE estimator given each possible value of Z and compute E[(X )]. Determine a function h so that = h(Z) is the MAP estimator given each possible value of Z and compute P(X ). Problem 24 Consider that X is a Poisson random variable with parameter = 1. Suppose that you make observations Z that are uncertain by an error with magnitude at most 2. For instance, if you observe {Z = 5} then you only know that X = {3, 4, 5, 6, 7}. Write a program to determine the function g so that MMSE estimator given each possible value of Z E[(X )]. Plot g(z) for 0 z < 20. = g(Z) is the and compute = h(Z) is the Write a program to determine the function h so that X MAP estimator given each possible value of Z and compute P(X ). Plot h(z) for 0 Z 20.