Let X have range [0,3] and density fX(x) = kx2. Let Y = X3. (a) Find k and the cumulative distribution function of X. (b) Find the 30th percentile of X. (c) Compute E(Y ). (d) Write down an explicit formula, involving an integral, for Var(Y ). (Do not compute the value of the integral.) (e) Find the probability density function fY (y) for Y .

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Let X have range [0,3] and density fX(x) = kx2. Let Y = X3.

(a) Find k and the cumulative distribution function of X.
(b) Find the 30th percentile of X.
(c) Compute E(Y ).
(d) Write down an explicit formula, involving an integral, for Var(Y ).
(Do not compute the value of the integral.)
(e) Find the probability density function fY (y) for Y .

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