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# If X is a random variable with probability density function f given by: f (x) = 4x 4x 3 when 0 x

If X is a random variable with probability density function f given by:

f (x) = 4x − 4x^{3}

when 0 ≤ x ≤ 1 and 0 otherwise, compute the following quantities:

(a) The cumulative distribution function F (X).

(b) The expectation E[X].

(c) The variance of X.

(d) The expectation of Y = 3 − X.

(e) The variance of Y = 3 − X

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