Negative Binomial Distribution

Probability mass function

Think of the question “What are the chances that I get 5 out of 15?” The negative binomial distribution can answer this for us.

These conditions must be met in order to be a negative binomial distribution;

  1. The experiment is a sequence of trials.
  2. The trials results can be characterized as successes or failures.
  3. The probability remains constant from one trial to the next. P( S on i ) = p
  4. The experiment continues until the desired number r successes have been observed.

The parameters needed to compute the probabilities mass function

  • x = number of failures we expect. N – r = x. Where N is the number of trials in the experiment.
  • r = the probability of this number of success is what we want to know.
  • p = probability for success.

Lets use a simple lottery example. I’m not going to use any tricky wording like you’re certain to find in texts and class.

Let’s say we have a lottery with a chance to win is .04

We want to know what are the chances we will win 3 times if we played 12 tickets.

Identify Our parameters : x = 12 – 3, r = 3, p = .04

Use our parameters as the function arguments and solve.

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