# Statistics Dictionary

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### Multinomial Experiment

A multinomial experiment is a statistical experiment that has the following properties:

• The experiment consists of n repeated trials.
• Each trial has a discrete number of possible outcomes.
• On any given trial, the probability that a particular outcome will occur is constant.
• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

Consider the following statistical experiment. You toss two dice three times, and record the outcome on each toss. This is a multinomial experiment because:

• The experiment consists of repeated trials. We toss the dice three times.
• Each trial can result in a discrete number of outcomes - 2 through 12.
• The probability of any outcome is constant; it does not change from one toss to the next.
• The trials are independent; that is, getting a particular outcome on one trial does not affect the outcome on other trials.

Note: A binomial experiment is a special case of a multinomial experiment. Here is the main difference. With a binomial experiment, each trial can result in two - and only two - possible outcomes. With a multinomial experiment, each trial can have two or more possible outcomes.