Question: The moment generating function of X is given by MX(t) = exp(2e^t 2) and that Y by MY (t) = ( (1/2)e^t + 1/2 )^10.

The moment generating function of X is given by MX(t) = exp(2e^t 2) and that Y by MY (t) = ( (1/2)e^t + 1/2 )^10. Assuming that X and Y are independent, find:

(a) (5 points). P(X + Y = 1).

(b) (5 points). E(XY ).

(c) (5 points). P(XY = 0).

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