Lesson 4.4 The Poisson Probability Distribution Function

Characteristics of the Poisson

A Poisson experiment is concerned with the number of times an event takes place in a particular interval. It is used extensively in the field of reliability.

The random variable X is equal to the number of times the event takes place in a particular interval.

μ = the average in the particular interval.

Notation and Formulae

The random variable X counts the number of times an event takes place in a particular interval. X takes on the values 0, 1, 2, 3, 4, ...

X follows a Poisson distribution with parameter m. We write this as:

X ~ P( μ )

Shortcut formulae:

mean: μ = np

Variance: σ ² = μ

Standard deviation: σ = square root of μ .

Back to Top

Poisson Problem Using the TI-83

Example: Suppose that the number of accidents in a week at a particular intersection is, on average, 1. The interval is one week so μ = 1.

Let X = the number of accidents that occur in one week at the intersection.

X takes on the values 0, 1, 2, 3, ....

The mean is μ= 1 so X ~ P(μ) becomes X ~ P(1).

Variance: σ² = μ = 1

Standard deviation: s = square root of 1 = 1 accident

Find the probability that 2 accidents occur in one week. (Find P(X = 2)). P(X = 2) = 0.1839 This calculation was done using TI-83 or TI-84 calculator function: 2nd DISTR B:possonpdf(1,2) Find the probability that at most 2 accidents occur in one week. (Find P(X <= 2)). At most means "less than or equal to." P(X <= 2) = 0.9197 This calculation was done by using TI-83 or TI-84 calculator function: 2nd DISTR C:poissoncdf(1, 2).

This is the last section of this lesson.

Back to Top

Up » 4.1 Discrete Probability » 4.2 Expected Value » 4.3 Binomial Probability » 4.4 Poisson Probability

Lesson 1 | Lesson 2 | Lesson 3 | Lesson 4 | Lesson 5 | Lesson 6 | Lesson 7 | Lesson 8 | Lesson 9 | Lesson 10 | Lesson 11 | Lesson 12