Question: Estimation of Random Variables 2 (5'3) (5 points each) X and Y are discrete random variables with joint probability mass function given by the table:

Estimation of Random Variables

2 (5'3) (5 points each) X and Y are discrete random variables with joint probability mass function given by the table: 'Where K is a nonnegative constant. a). Find the numerical value of K. b). Find the marginal PMFs PX (n) and p1: (n) for all values of n. c). Find the characteristic function le (a!) . d). Find the best constant minimum MSE estimator if: for X given 1'. c). Find the best homogeneous linear minimum MSE estimator XALH for X given 1'. . Find the best non-homogeneous linear minimum MSE estimator it for X given F. g). Find the best nonlinear minimum MSE estimator jam for X given 1'. h). Find the best maximum likelihood estimator Km for X given Y. i). Find the best maximum a posteriori estimator KIM for X given Y. j). Find the minimum meansquare error of parts t]. and g). only

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