8. Consider the probability density function for a continuous random variable X, 0 {2e-2/3 if OSIS M 0 otherwise f(x)= = (a) What must the value of M be to ensure that f(x) is in fact a probability density function of X? (A) 2ln(3) (D) 3 ln(3) (E) [infinity] (B) In (3) (B) In (3) (C) 3 ln(2) (C) 3 ln(2) (b) Determine the cumulative distribution function of f(x) on the interval x = [0, M]. (c) Suppose we wish to generate random numbers in this distribution. What function must we pass uniform (0, 1) random numbers through to generate such random numbers?