The following table gives pxynbspx y the joint probability, Ask an Expert

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The following table gives P_X,Y (x, y), the joint probability mass function of random variables X and Y.

(a) Find the marginal probability mass functions P_X (x) and P_Y (y).

(b) Are X and Y independent?

(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 e_L.

(e) What is e∗_L, the minimum mean square error of the optimum linear estimate?

(f) Find P_X|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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Statistics and Probability, Statistics

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