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A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...

A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise

(a) Find the value c such that f(x) is indeed a density function.

(b) Write out the cumulative distribution function of X.

(c) P(1 < X < 3) =?

(d) Write out the mean and variance of X.

(e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.

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