5 Change of Variables

When continous random variable X has density f(x), we can define a new random variable Y=g(X) by applying some function to X. What is the density of this new random variable? If the function g is one to one and differentiable, then the answer is given by the Change of Variables Formula, which is discussed here.

S1: C-o-V Formula

S2: Location-Scale Families

S3: General Normal Distributions

S4: Square of a Normal RV

S5: The Probability Integral Transformation.