Variable Transformations

This lecture covers the transformation of distribution and density functions when considering variable transformations, summarizing the results by defining a new random variable Y as a function of X. It explains the calculation of the new random variable's cumulative distribution function and density function, both in continuous and discrete cases. The lecture also discusses the comparison between discrete and continuous random variables, highlighting differences in support, density functions, and probabilities. The importance of non-negativity and normalization of density functions is emphasized, along with the definition of cumulative distribution functions and probabilities for both types of random variables.