Reference no: EM131083747
The following table gives PX,Y (x, y), the joint probability mass function of random variables X and Y.
(a) Find the marginal probability mass functions PX (x) and PY (y).
(b) Are X and Y independent?
(c) Find E[X], Var[X], E[Y], Var[Y], and Cov[X, Y].
(d) Let 
(Y) = aY + b be a linear estimator of X. Find a* and b*, the values of a and b that minimize the mean square error eL.
(e) What is e∗L, the minimum mean square error of the optimum linear estimate?
(f) Find PX|Y (x| - 3), the conditional PMF of X given Y = -3.
(g) Find 
M (-3), the optimum (nonlinear) mean square estimator of X given Y = -3.
(h) What is
The mean square error of this estimate?
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