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Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0...

Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0 < ? < 2.

(a) Find the constant c.

(b) Find the cumulative distribution function (CDF) of X.

(c) Find P(X < 0.5), and P(X > 1.0).

(d) Find E(X), Var(X) and E(X5 ).

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