Probability and Random Variables

In this course probability and random variables are thought. First, the basic concepts from of probability concepts such as experiment, sample space, events are explained. Then, repeated trials, permutations, combinations, and multiplication rule, etc. are explained. Following basic topics of probability, random variables are introduced. Probability mass functions are explained by examples. Well known probability distributions, such as Bernoulli, uniform, poisson etc, are examplified. Cumulative distribution function, joint distribution, and calculation of joint distribution functions are taught.  A random variable is continuous if possible values comprise either a single interval on the number line or a union of disjoint intervals.

Discrete random variables can take only a countable number of possible values. On the other hand, a continuous random variable has a range in the form of an interval or a union of non-overlapping intervals on the real line (possibly the whole real line).  Thus, we need to develop new tools to deal with continuous random variables. The good news is that the theory of continuous random variables is completely analogous to the theory of discrete random variables. After studying the discrete random variables, we focus on continuos random variables, and introduce probability density function. Then, we cover the same set of topics as it is done for discrete random variables.