Probability Functions
There are two types of functions to display the probability attributed to each outcome. These display the probabilities as areas, which as we discovered, works well for continuous probability problems.
Probability Mass Function
A Probability Mass Function shows the probability attributed to discrete probability distributions. Each outcome should appear on the x axis, and the bar for each outcome will be the length of the probability of this outcome. For example, the probability mass function for a standard, fair, 6-sided die would be 6 bars (labeled 1 to 6), where each bar starts at zero and ends at $\frac{1}{6}$
Here is a link to a Desmos chart of the Probability Mass Function of the example described above.
Probability Density Function
A Probability Density Function shows the same information, but for a continuous probability problem. Remember that we use area to represent probability, so the probability that a range of values occurs is the area of that region under the curve.
This 3Blue1Brown video does an excellent job diving into the Binomial Distribution, but the ideas in this video about probability density functions apply to any distribution.
Common Distribution Functions
While the Binomial distribution was mentioned in the previous video, the most well known and often-used distribution is the Normal distribution, also known as the Gaussian distribution, or sometimes "the bell curve," which describes a surprising number of situations.
We'll explore the Normal distribution more in the section on Random Variables next module.