Notes on Statistics

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Topic #1. Distributions of functions of random variables
Given random variables drawn from some known distribution, and a function of these random variables. We are interested in finding the distribution of this function's value. We are going through three techniques to find the probability distributions of random variables: distribution function technique, change of variable technique and moment-generating function technique.

First, we consider function of one random variable with two techniques: distribution function technique and change of variables technique. Then, we extend the same technique to transformation of two random variables. Next, we consider cases where the random variables are independent, and sometimes identically distributed. After that, we spend sometimes with the third technique, moment generating function, to find the distribution of functions of random variables.

- Source
     1) https://onlinecourses.science.psu.edu/stat414/node/127
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