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Suppose that X has probability function fX(x)=cx2   for 0<x<1. (a) (5 pts) Find c. (b) (5...

Suppose that X has probability function fX(x)=cx2   for 0<x<1.

(a) (5 pts) Find c.

(b) (5 pts) Compute the cdf, FX(x).

(c) (5 pts) Find P(-1 ≤ X ≤ 0.5) .

(d) (5 pts) Find the moment-generating function(mgf) of X.

(e) (10 pts) Use the mgf to find the values of (i) the mean and (ii) the variance of X.

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