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5) Let X1, X2, and X3 be independent random variables with the following probability density function,...

5) Let X1, X2, and X3 be independent random variables with the following probability density function, f(x) = 2 − 2x for 0 < x < 1; f(x) = 0 otherwise.

a) Find the probability that X1 exceeds 1/2. b) Find the probability that exactly one of the three variables exceeds 1/2.

6) The pdf of X is fX(x) = 4xe−2x , x > 0. a) Find E(X). b) Find Var(X).

7) The joint pdf of X and Y is fXY (x, y) = cx2y, x2 ≤ y ≤ 1 and fXY (x, y) = 0 otherwise. a) Find c. b) Find P(X ≥ Y ). c) Find the marginal pdf fY (y)

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