# Binomial Distribution

Binomial Distribution The binomial distribution is a discrete distribution. Recall that the binomial distribution applies to a very specific situation: when a number of independent and identical trials occur, and each trial results in a success or failure. Then the binomial random number is the number of successes in these trials. The two parameters of this distribution, n and p, are the number of trials and the probability of success on each trial.

As an example, suppose an airline company sells 170 tickets for a flight and estimates that 80% of the people with tickets will actually show up for the flight. How many people will actually show up? It is tempting to state that exactly 80% of 170, or 136 people, will show up, but this neglects the inherent randomness. A more realistic way to model this situation is to say that each of the 170 people, independently of one another, will show up with probability 0.8. Then the number of people who actually show up is then binomially distributed with n 5 170 and p 5 0.8. (This assumes independent behavior across passengers, which might not be the case, for example, if whole families either show up or don’t.)

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A random number from a binomial distribution indicates the number of successes in a certain number of identical trials.

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