Basic Concepts of Probability Theory

We will start our way of learning probability theory by considering some basic definitions and rules: what is a stochastic experiment and random event, what is independence and incompatibility of events in the context of probability theory, what is the probability and how can we calculate probabilities of different elementary events.

Probability of Complex Events

In real-life tasks, we often have to deal with complex relationships and, as a result, calculate probabilities of several events or events that depend on each other. Let's consider how we can do this using probability theory.

Commonly Used Discrete Distributions

To solve many real problems in probability theory, special models have been created that describe a particular situation. Let's consider some of the most used models that can be used to describe some discrete results of stochastic experiments.

Commonly Used Continuous Distributions

What if the result of a stochastic experiment cannot be described by a discrete value? For this, models that work with continuous values are used. Consider the most popular of these models.

Covariance and Correlation

Often we are faced with the task of checking the dependence of the results of different stochastic experiments on each other. Moreover, it is necessary not only to assess the presence of dependencies but also to somehow quantify the degree of dependencies. To solve these problems, we can use covariance and correlation.