# TI-BASIC:Poissonpdf

**Command Summary**

Calculates the Poisson probability for a single value

**Command Syntax**

poissonpdf(*mean*, *value*)

**Menu Location**

Press:

- 2ND DISTR to access the distribution menu
- ALPHA B to select poissonpdf(, or use arrows.

Press ALPHA C instead of ALPHA B on a TI-84+/SE with OS 2.30 or higher.

TI-83/84/+/SE

2 bytes

This command is used to calculate Poisson distribution probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

- A specific event happens at a known average rate (X occurrences per time interval)
- Each occurrence is independent of the time since the last occurrence
- We're interested in the probability that the event occurs a specific number of times in a given time.

The poissonpdf( command takes two arguments: The *mean* is the average number of times the event will happen during the time interval we're interested in. The *value* is the number of times we're interested in the event happening (so the output is the probability that the event happens *value* times in the interval).

For example, consider point on a city street where an average of 5 cars pass by each minute. What is the probability that in a given minute, 8 cars will drive by?

- The event is a car passing by, which happens at an average rate of 5 occurrences per time interval (a minute)
- Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
- We're interested in the probability that the event occurs 8 times in the time interval

The syntax in this case is:

:poissonpdf(5,8

This will give about .065 when you run it, so there's a .065 probability that in a given minute, 8 cars will drive by.

# Formulas

The value of poissonpdf( is given by the formula

<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \operatorname{poissonpdf}(\lambda,k) = \frac{e^{-\lambda}\lambda^k}{k!} </math>