Intro To Probability Distribution 2

What is a Probability Distribution?

Probability distributions allow you to represent the probability of an event using a mathematical equation. Like any mathematical equation:

probability distributions can be visualized using a graph especially in 2-dimensional cases.
probability distributions can be worked with using algebra, linear algebra and calculus.

These distributions make it much easier to understand and summarize the probability of a system whether that system be a coin flip experiment or the location of a self-driving car.

Types of Probability Distributions

Probability distributions are really helpful for understanding the probability of a system.
Looking at the big pictures, there are two types of probability distributions:

discrete probability distributions
continuous probability distributions

Before we get into the details about what discrete and continuous mean, take a look at these two visualizations below. The first image shows a discrete probability distribution and the second a continuous probability distribution. What is similar and what is different about each visualization?

Discrete Distribution (left) and Continuous Distribution (Right)

Discrete and continuous distributions

Based on the visualizations, which of the following are true about the discrete probability distribution versus the continuous probability distribution?

For both visualizations, the y-axis represents the probability of an event occurring (hint: look at the y-axis labels).

The x-axis represents the main variable of interest for both visualizations.

In the discrete visualization, the x-axis variable can only take on certain values such as 1, 2 or 3.

In the discrete visualization, the x-axis variable can take on any value such as 3.4 or 0.5.

In the continuous visualization, the x-axis variable can take on any real number value from -infinity to +infinity.

For the discrete visualization, the y-axis represents the probability of an event occurring (hint: what does the y-axis label say?).

SOLUTION:

The x-axis represents the main variable of interest for both visualizations.
In the discrete visualization, the x-axis variable can only take on certain values such as 1, 2 or 3.
In the continuous visualization, the x-axis variable can take on any real number value from -infinity to +infinity.
For the discrete visualization, the y-axis represents the probability of an event occurring (hint: what does the y-axis label say?).