Multinomial Distribution
Overview
- The Multinomial distribution is a generalization of the Binomial distribution to multiple categories.
- It describes the probability of observing a specific combination of outcomes across multiple categories in a fixed number of trials.
Use Case
- Used when conducting a fixed number of independent trials with more than two possible outcomes in each trial, such as rolling a multi-sided die or categorizing items into multiple classes.
- Probability Mass Function (PMF):
- : Number of observations in category
- : Number of observations in category
- : Probability of category
- : Total number of trials
- : Number of categories
Example
- Dice Rolling:
- Suppose we roll a fair 6-sided die 10 times.
- We want to find the probability of getting 2 ones, 3 twos, 4 threes, and 1 four.
- Let , , , and be the probabilities of each outcome.
- Using the Multinomial PMF:
