Statistics for Business: Decision Making and Analysis, 3rd Edition

11.1 Random Variables for Counts

Let’s restate the questions posed in the introduction using a random variable. In this chapter, the random variable Y denotes the number of doctors a detail rep meets during 10 office visits. The question, “How many doctors should a rep be expected to meet?” asks for the mean of Y, E(Y). The second question, “Is a rep who meets 8 or more doctors doing exceptionally well?” requires P(Y ≥ 8). To find these properties of the random variable, we’ll identify a pattern that’s common to many counting problems. The pattern represents Y as a sum of simple random variables that take on only two possible values, zero and one.

Bernoulli Random Variable

We will treat a visit to a doctor’s office as a chance event with two ...