Question: Random variables X and Y have joint PMF (a) Find the marginal probability mass functions PX(x) and PY(y). (b) Are X and Y independent? (c)

Random variables X and Y have joint PMF
Random variables X and Y have joint PMF (a) Find the

(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].

Random variables X and Y have joint PMF (a) Find the

(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.

Random variables X and Y have joint PMF (a) Find the

(h) Find the mean square error

Random variables X and Y have joint PMF (a) Find the

of this estimate.

Pry(z,v) y 1/63 y 1/81 1/24 30 =-1|1/6 1/81/24 z=0 | 1/12 1/121/121/12 r=1 | 0 1/241/81/6 T M

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