Question

A general method for simulating a random variable—called the inverse transformation method—is based on the following function:
F^ −1 (u)= min{x : F(x)≥ u } where F is a distribution function and 0 < u < 1 .
(a) Showthat F^−1(u)≤x⇔u≤F(x)forall u∈(0,1)andreal x.
(b) Use the result in (a), or otherwise, to show that if F is a distribution function and U is a
uniform random variable from (0,1), then X = F ^−1 (U ) will be a random variable with
distribution function F.
(c) Write down the procedure to generate a random variable from Exp(λ).