April 2026
Beginner
288 pages
5h 34m
English
Content preview from Probability Workbook For Dummies
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Chapter 15
Making a Positive Out of the Negative Binomial Distribution
IN THIS CHAPTER
Recognizing the characteristics of a negative binomial distribution
Calculating probabilities for the negative binomial
Determining the negative binomial’s mean, variance, and standard deviation
The negative binomial distribution is a more general version of the geometric distribution discussed in Chapter 14. Instead of counting the total number of trials until the first success, you count the number of trials until the kth success, where k is any number from 1, 2, 3, and so on. For example, the geometric distribution counts the number of flips of a coin until the first head appears, but the negative binomial distribution counts the number of flips of a coin until the third heads (or fourth heads or tenth heads, and so on).
Perhaps it is called a negative binomial because, in a way, it’s the opposite of a regular binomial distribution (see Chapter 8). The binomial fixes the number of trials and counts the number of successes within those trials; for example, you flip a coin 25 times (the fixed part) and get heads (the random part). Whereas the negative binomial fixes the number of successes ...
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