EXAMPLE 1 Identifying a Multinomial Random Variable

For each of the following, determine whether the random variable is multinomial.

  1. We select 10 students at random and define our random variable to be the amount of time the student used a Web browser yesterday.
  2. We select 10 students at random and define our random variable to be the browser used most by the student the last time he or she was on the Internet, where the possible values are Google Chrome, Microsoft Internet Explorer, or Other.

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Solution

  1. The amount of time spent using a browser is a continuous random variable, not categorical. So, cannot be multinomial.
  2. The browser is categorical. We have different categories, with the population proportions of the three categories adding up to one (see Example 2(a) below). Therefore, is multinomial.

NOW YOU CAN DO

Exercises 5–8