Let X be a random variable with probability density function (pdf):

f(x) = ( C x 5/2 if x 2 0 x < 2 (a) [3] Find the constant, C, and the median of X.

(b) [2] Find the cumulative distribution function (cdf), FX(x) of X.

(c) [3] Find the expected value and variance of X (if they exist).

(d) [2] If g(x) = min(x, 2), compute the expected value E [g(X)].