Question: Let X and Y be two discrete random variables, with joint PMF: pX,Y (x, y) = c(x2 +y2) = 0 if x{1,3,4} and y{2,3} otherwise

Let X and Y be two discrete random variables, with joint PMF:

pX,Y (x, y) = c(x2 +y2)

= 0 if x{1,3,4} and y{2,3} otherwise

(a) (5 points) Find the value of c.

(b) (5 points) Find P(Y < X).

(c) (5 points) Find the PMF of X.

(d) (5 points) Find the variance of X.

(e) (5 points) Find E[XY ].

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