Introduction to Random Variables

ACCESS the FULL COURSE here: https://academy.zenva.com/product/data-science-mini-degree/?zva_src=youtube-datascience-md

TRANSCRIPT

Hello everybody. We are going to talk about hypothesis testing. But before we quite get into that, we have to know a little bit of background information in order to do hypothesis testing. In specific, we have to know a little bit about random variables and probability distributions, as well as a very important distribution called the normal distribution, as well as a very important theorem called the central limit theorem. And all these things gonna to tie together when we get into doing hypothesis testing. We're going to use all these quite extensively. So the first thing we need to talk about are random variables. So, a random variable is just a variable whose value is unknown. Another way you can think about this is, a variable that is the outcome of some kind of statistical experiment. So I have two examples here, say Let X equal a single coin toss. So we don't know what X, we don't know what the value of X is, but we know all of the possible values that it can take on. We just don't know what the actual value is, because it is a random variable. But we can say that, well the probability that X is gonna be heads is a half, the probability that X is gonna be tails is also a half. We don't know what the actual value is, but we know about all the values it can take on. In other words, we call this the domain of a random variable. For these variables here, it is the different values that it can take. So, think of a dice toss that I have here. We have possible values here that X can be one, two, three, four, five, or six, and each of these are equally likely. And just a point on notation is that this capital X is the random variable, if you see lowercase x that usually means a very specific value of the random variable. Speaking of random variables, we can broadly separate them into two different categories. We have discrete random variables and continuous random variables. So discrete random variables, as the name implies, can only take on a countable number of values. So, picture things like doing a coin toss or a dice roll. They're very discrete number values. Using this interesting example, that's used a lot in statistics textbooks, it's a seminal problem that you'll see in statistics textbooks. If you've taken a course on statistics, you'll probably have some question like this, the number of defective light bulbs in a box of 100. So the different outcomes here are: Light bulb one is defective or not, light bulb two is defective or not, light bulb three is defective, and so on and so on. This is an example of a discrete random variable. So, we have discrete random variables and we also have continuous random variab ... https://www.youtube.com/watch?v=rG-Uvmf94s4