ABSTRACT
In this chapter, the authors introduce random variables and their properties starting with their application to games of chance. They can easily generate random variables using some of the simple examples the people have shown. In this case, the distribution of that list is the probability distribution of X and the average and standard deviation of that list are the expected value and standard error of the random variable. However, the authors focus on the CLT, which can be generally applied to sums of random variables in a way that the binomial distribution can't. If a random variable has probability distribution that is approximated with the normal distribution, then all the people need to describe the probability distribution are the average and standard deviation, referred to as the expected value and standard error. The square of the standard error of the sum of independent random variables is the sum of the square of the standard error of each random variable.
