The joint PMF, pX,Y(x,y), of the random variables X and Y is given by the following table:

Question

(see: the science of uncertainty)

1. Find the value of the constant c.
c = 0.03571428571428571428

2. Find pX(1).
pX(1)= 1/2

3. Consider the random variable
Z=X2Y3. Find E[Z∣Y=−1].
E[Z∣Y=−1]= -1.7142857143

4. Conditioned on the event that Y≠0,
are X and Y independent? YES

5. Find the conditional variance of Y
given that X=0.
var(Y|X=0)= 0.8888888889