Statistical Models: Families and Transformations

This lecture covers statistical models, focusing on families of distributions and transformations. It discusses exponential families, natural vs. usual forms, examples like the binomial and Gaussian families, and probability models. The lecture also explores probability transformations, including discrete and continuous cases, affine transformations, and multidimensional transformations. Applications such as convolutions of densities and sums of normal random variables are presented, along with relevant corollaries.