Assume that a source of U(0, 1) random numbers U1, U2, ... is readily available. Consider the following probability density function of the continuous random variable X, where the value of k has not yet given: f(x) = {k (2x²³ + x), if 0 ≤x≤ı, otherwise. (b) Determine the cumulative density function F(x) of X for all -∞0 < x < ∞. (c) Construct an algorithm for generating independent and identically distributed random variates for X by the composition method. Show all steps explicitly and clearly.