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1. Let X be a random variable with PMF

x 0 1 2 3 4

p(x) 5k 4k 3k 2k k

(a) Find k.

(b) Find E[X] and var(X).

(c) Find E[2^X].

2. The joint PMF of X and Y is pX;Y (x; y) = c(x2 + y2), x; y = 1; 2; 3. Find

(a) c and the marginal PMFs of X and Y

(b) E[X]

(c) The PMF of 3X - 2Y

(d) E[3X - 2Y ] in two ways.

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# Probabilty question !

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