Consider the integral: I = f sm(2x)cos2(m)e"mds (1) 0 (a) I = E[sin(2:r:)(cos 3:)3] for a random variable X. What is the CDF of X. (b) Assume that we have a technology for generating a random number U from U ml f orm( 0, 1). Obtain a transformation g(U) that has the same distribution as the random variable X in (a). (c) Using (b) above, write an algorithm for generating independent observations X1, X 2, ..., Xn (where n is large), and use Xn to approximate I in (a). (d) Using Weak Law of Large numbers and CLT, how accuaret is the approximation in (c)