g Let X be a continuous random variable with pdf f(x) = ( k x4 x > 1 0 x ≤ 1 (a) (5 points) Determine the value of k for which f(x) is a legitimate pdf. (b) (5 points) Obtain the cumulative distribution function. (c) (5 points) Use the cdf from (b) to determine the probability that X is greater than 2. (d) (5 points) Obtain the expected value and variance of X.