Course Content

# Probability Theory Basics

4. Commonly Used Continuous Distributions

5. Covariance and Correlation

Probability Theory Basics

## Gaussian Distribution

The **Gaussian distribution**, also known as the **normal distribution**, is a continuous probability distribution widely used in statistics and probability theory. We can use this distribution to describe the following values:

*Physical Measurements*: Many physical measurements, such as height, weight, blood pressure, and body temperature, can be reasonably approximated by a Gaussian distribution. For example, the height of adult men or women in a population often follows a Gaussian distribution.*Errors and Residuals*: In statistical analysis or regression modeling, errors or residuals (the difference between observed and predicted values) are usually assumed to be normally distributed.*Test Scores*: Standardized test scores such as the SAT or ACT are often modeled using a Gaussian distribution in educational testing.*Environmental measurements*: A Gaussian distribution can often describe variables such as air pollution, noise levels, and water quality measurements.

We can also use `.cdf()`

method of `scipy.stats.norm`

class to work with Gaussian distribution in Python. It has two main parameters: `loc`

determines the mean value of the experiment's result, and `scale`

determines the average deviation from the mean.

Let's consider an example:

Calculate the probability that the height of a randomly chosen man will be less than `160`

or more than `190`

. Assume that the mean value of men's height is `170,`

and the average deviation is `20`

.

The Gaussian distribution is one of the most popular and commonly used distributions. Its properties are discussed in more detail in the Probability Theory Mastering course..

Everything was clear?