EXAMPLE 2 Finding the expected frequencies

According to the Adobe Digital Index, the market share for the leading Internet browsers (both desktop and mobile) in June 2014 was as shown in Table 1. Let of a randomly selected Internet user.

  1. Verify that is a valid multinomial random variable.
  2. Find the expected frequency for each category in a series of 200 trials.
Table 11.1: Table 1 Distribution of browser market share
Browser Relative frequency
Google Chrome 0.32
Microsoft Internet Explorer 0.31
Other 0.37

Solution

  1. There are possible outcomes: Google Chrome, Microsoft Internet Explorer, and Other. Assigning probabilities using the relative frequency method, we have the following hypothesized proportions for each browser:

    and

    Therefore, is a valid multinomial random variable.

    634

  2. We have trials (), so the expected frequencies are as provided in Table 2.
Table 11.2: Table 2 Expected frequencies for browser preference in sample of size 100
Category
Google Chrome
Microsoft Internet Explorer (IE)
Other

As a check on the calculations, we should have . In this case,

NOW YOU CAN DO

Exercises 9–12.