I am trying to use the Inverse Transform Method to generate samples from this equation 1/12 * cube root of x where 0<=x<8. I have tried following some of the tutorials on the site with no success, please help me. I am trying to revise for an end of semester examination. How do I use the steps below to generate samples from the equation. Pardon my equation expressed in words I do not know how to use the formatting tools provided by the site to format the expression
a) Let F(x), x E R denote any cumulative distribution function
b) Let F−1(y)F−1(y), y∈[0,1]y∈[0,1] denote the inverse function and define X=F−1(U)X=F−1(U), where U∼U(0,1)U∼U(0,1)
c) Generate u∼U(0,1) u∼U(0,1).
d) Set u=1−e−0.05xu=1−e−0.05x (CDF of Exponential)
e) Solving for x, yields: x=−10.05log(u)