Probability Distributions - An Introduction

Introduction

We have learned that probability gives us the percent chance of an event occurring. Now, what if we want an understanding of the probabilities of all the possible values in our experiment? This is where probability distributions come into play.

A probability distribution is a function that represents the probabilities of all possible values. This is a very important concept in data science, by specifying the relative chance of all possible outcomes. Probability distributions allow us to understand the underlying trends in our data. For example, if we have some missing values in our dataset, we can understand the distribution of our data using probability distributions and then replace missing values with the most likely values.

Random Variables

For the next couple of lessons, we are going to look at some of the most important probability distributions. But before we dive into probability distributions, we need to understand the different types of data we can encounter.

The set of possible values from a random experiment is called a Random Variable. Random Variables can be either discrete or continuous:

• Discrete Data (a.k.a. discrete variables) can only take specified values. For example, when we roll a die, the possible outcomes are 1, 2, 3, 4, 5, or 6 and not 1.5 or 2.45.
• Continuous Data (a.k.a. continuous variables) can take any value within a range. This range can be finite or infinite. Continuous variables are measurements like height, weight, and temperature.

Types of Probability Distributions

Since probability distributions describe the distribution of the values of a random variable, the kind of variable determines the type of probability distribution we are dealing with. This means that probability distributions can be divided into the following two types:

• Discrete probability distributions for discrete variables
• Probability density functions for continuous variables