There is one theorm in my Applied Probability course that I am having trouble understanding. It has to do with how to derive various types of random variables from the transformation X= g(U)
It says, Let U be a uniform (0,1) random variable and let F(x) denote a cumulative distribution function with an inverse F^-1(u) defined for 0<u<1. The random variable X = F^-1(U) has a CDF FX(x) = F(x).
I think my lack of understand of what F^-1(u) is hindering my understanding of this theorm. Would you be able to explain?
From what I understand and the examples looked at, this theorm allows us
derive random variables of different types, using the uniform random