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The Beta distribution with parameters a = 3, b = 2 has PDF f(x)=12x2(1−x), for 0 < x < 1.

Let X have this distribution.

(a) Find the CDF of X.

(b) Find P(0 < X < 1/2).

(c) Find the mean and variance of X (without quoting results about the Beta distribution).

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