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Categorical Distribution

TL;DR

Models probabilities for a finite set of discrete categories (outcomes).
Probabilities are determined from counts or assigned weights for each category.
Commonly used to represent outcomes like coin tosses, card colors, or colored objects in a bag.

Definition

Categorical distribution is a type of probability distribution that involves a set of possible categories or outcomes. It is often used to model the probability of an outcome occurring within a certain category.

Explanation

A categorical distribution assigns a probability to each possible category in a finite set of outcomes. The probability of an outcome can be determined by the number of favorable items divided by the total number of items in the sample space, as illustrated in the examples below.

Examples

Example 1

A bag contains 10 red marbles and 20 blue marbles. If a marble is randomly selected, the possible outcomes are red or blue, and the probability of selecting a red marble is: $\frac{10}{30} = 0.33$

Example 2

A standard deck has 52 cards. If a card is randomly selected, the possible outcomes include red or black, and the probability of selecting a red card is: $\frac{26}{52} = 0.5$

Example 3

A bag contains 10 red balls, 20 blue balls, and 30 green balls. If a ball is randomly selected, the possible outcomes are red, blue, or green. The bag has a total of 60 balls, and the probability of selecting a red, blue, or green ball is described in the source as: $\frac{10 + 20 + 30}{60} = 1$

Use cases

Modeling the probability of an outcome occurring within a specific category (e.g., coin tosses, card colors, colored objects in a bag).

Probability distribution