Answered You can hire a professional tutor to get the answer.
Consider the distribution function F(X):
1. Consider the distribution function F(X):0 for x < − 11/10 for -1 ≤ x < 2 x^3/48 for for 2≤x<39(x-1)^2/64 for 3≤x<11/3 1 for x ≥ 11 / 3a) Assuming that a uniform random number generator is available, use the inversion method to provide an algorithm for generating a random variable X having distribution function F .---I think I understand this part, but am really struggling with the rest of the question---b) Compute E[ X ] and Var[ X ] analytically.c) Prove the following converse of the inversion method: if X is a random variable having acontinuous, strictly increasing distribution function F, then U = F ( X ) is uniformly distributed on [0,1]. [Hint: the assumptions on F ensure that F−1 (F(x))= x for any real number x, andF(F−1(y))= y for any y∈[0,1]. Also note that both F and F−1 are nondecreasing functions.]
