Question: Consider two random variables X and Y with joint PMF given in Table 5.2. Let Z = E[X|Y]. a. Find the Marginal PMFs of X

Consider two random variables X and Y with joint PMF given in Table 5.2. Let Z = E[X|Y].

a. Find the Marginal PMFs of X and Y .

b. Find the conditional PMF of X given Y = 0 and Y = 1, i.e., find PX|Y (x|0) and PX|Y (x|1).

c. Find the PMF of Z.

d. Find EZ, and check that EZ = EX.

e. Find Var(Z).X = 0 X=1 Y=0 116 25 Y=1 0

X = 0 X=1 Y=0 116 25 Y=1 0

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