Probability Theory

Here, you find my whole video series about Probability Theory in the correct order and I also help you with some text around the videos. If you want to test your knowledge, please use the quizzes, and consult the PDF version of the video if needed. When you have any questions, you can use the comments below and ask anything. However, without further ado let’s start:

Probability Theory is a video series I started for everyone who is interested in stochastic problems and statistics. We can use a lot of results that one can learn in measure theory series. However, here we will be able to apply the theorems to probability problems and random experiments. In order to this, we will use RStudio along the way:

With this you now know the topics that we will discuss in this series. Some important bullet points are probability measures, random variables, central limit theorem and statistical tests. In order to describe these things, we need a good understanding of measures first. They form the foundation of this probability theory course but we do not need to go into details. Now, in the next video let us discuss probability measures.

The notion of a probability measure is needed to describe stochastic problems:

We distinguish discrete and continuous cases because they often occur in applications:

Now we talk about a special discrete model: the binomial distribution. It occurs when we toss a coin n times and count the heads. Alternatively, we could draw n balls, with replacement, from a urn with two different kinds of balls: