Universality of the uniform

2021 May 19 See all posts

Universality

Given UU uniformly distributed over (0,1)(0,1), and XX with CDF FF

F1(U)=XF^{-1}(U) = X and F(X)=UF(X) = U

Visually

TODO

  1. Briefly explain random variables, probability distributions with examples
  2. Explain the uniform distribution
  3. Show transformations on the uniform CDFs
  4. Show with the PDFs