# Multinomial Process

A Multinomial Process, $\displaystyle{ B(n, p) }$, is a compound random experiment composed of $\displaystyle{ n }$ mutually independent multinomial trials with $\displaystyle{ p }$ probability mass function.

## References

### 2009

• http://stattrek.com/Tables/multinomial.aspx#experiment
• A multinomial experiment is a statistical experiment that has the following characteristics:
• The experiment involves one or more trials.
• Each trial has a discrete number of possible outcomes.
• On any given trial, the probability that a particular outcome will occur is constant.
• All of the trials in the experiment are independent.
• Tossing a pair of dice is a perfect example of a multinomial experiment. Suppose we toss a pair of dice three times. Each toss represents a trial, so this experiment would have 3 trials. Each toss also has a discrete number of possible outcomes - 2 through 12. The probability of any particular outcome is constant; for example, the probability of rolling a 12 on any particular toss is always 1/36. And finally, the outcome on any toss is not affected by previous or succeeding tosses; so the trials in the experiment are independent.
• A multinomial distribution is a probability distribution. It refers to the probabilities associated with each of the possible outcomes in a multinomial experiment. For example, suppose we toss a toss a pair of dice one time. This multinomial experiment has 11 possible outcomes: the numbers from 1 to 12. The probabilities associated with each possible outcome are an example of a multinomial distribution