Chapter 14, Problem 32SE

To determine

List the characteristics of a multinomial experiment.

Explanation of Solution

Properties of a multinomial experiment:

• The experiment has n identical trials.
• The outcome of each trial falls into one of k classes.
• The probability that the outcome of a single trial falls into cell i is $p_i$ for $i=1,2,\mathrm{...}k$ and remains the same from trial to trial.
• The trials are independent.
• $Y_1,Y_2,\mathrm{...},Y_k$ are a random variables of interest, where $Y_i$ is equal to the number of trials for which the outcome falls into cell i.