In our course, we will study random variables. Random variable can be used to model some natural phenomenas. It is the main tool that we'll use to study our data. But what is random variable? To answer this question, let us consider some casino. This is world-famous, because you know the Monte Carlo. I have never been in this place, but I can imagine how it looks. Sound well-dressed people, make their beds on different games like roulette, or blackjack. This is a perfect example of some random variables. Indeed, consider all that. You probably know how it looks like. There is a wheel with 37 sectors, and on each sector there is a number, and some sectors are red, and some sectors are black. There is a special sector which is called zero, and it is green, and people can make different bets. For example, one player can bet for a particular number, for example 23. Another player can bet for example for even, or for red, and there are other examples on bets. Consider Alice; Alice bets $100 on red. It means that if the small bowl that spins inside this wheel stops in red sectors, then she wins, and her winning is $100. But in other case, if the ball stops in the x sector, then she lose her $100. There is a special case, when balls stops at zero. In this case she loses $50, half of her bet. When I described this roles, I didn't give you information on what will be exact payout of Alice after one spinning of the wheel. But you'll understand how these payout works in probabilistic terms. You can answer different probabilistic questions. For example, what is the probability that Alice wins some positive amount of money? You can find it by calculation. So Alice payout is an example of a random variable. That is a variable which rarely depends on the result of some random experiment. In this case, random experiment is the spinning of this roulette. This is actually informal definition of the notion of random variable. Random variable denotes some value that depends on the result of some random experiment. So to define a random variable, we have to describe random experiment in some way. Of course, random variables are not limited to gambling. We will use them to model a lot of different natural phenomenas. For example, how many people will finish this course? I don't know exactly, but I can propose some model that will involve random variable for this number. What will be your final grade? It is also a kind of random variable because we don't know in advance what will be this value. What will be the price of bitcoin tomorrow? A lot of people want to know this value, but nobody can. It is an example of a random variable as well. What will be opening weekend box office for particular new film? Again, a lot of people interested in this value, and nobody knows the exact value before we conduct our random experiment, before we perform this film for the first weekend, and get the actual area. So let us discuss what will we study at the lesson. First of all, we consider some more examples of random variables, just to have some examples to begin with.Then we will discuss that there are two kinds of random variables, that will be discussed in our course; discrete random variables and continuous random variables. During this week we will discuss discrete random variables. Then we will discuss how to define and describe random variables, and how we can visualize them. We will also study some important distributions of random variables like binomial distribution. We will discuss some properties of random variables like expected value and variance. Finally, we will use python to generate and study on random variables. So let us begin.