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Let X be a random variable with pdf given by fX(x) = Cx2(1−x)1(0 < x <...

Let X be a random variable with pdf given by fX(x) = Cx2(1−x)1(0 < x < 1), where C > 0 and 1(·) is the indicator function.
(a) Find the value of the constant C such that fX is a valid pdf.

(b) Find P(1/2 ≤ X < 1).

(c) Find P(X ≤ 1/2).

(d) Find P(X = 1/2).

(e) Find P(1 ≤ X ≤ 2).

(f) Find EX.

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