The poissonpdf( Command Command Summary

Calculates the Poisson probability for a single value

Command Syntax

poissonpdf(mean, value)

Press:

1. 2ND DISTR to access the distribution menu
2. 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:

1. A specific event happens at a known average rate (X occurrences per time interval)
2. Each occurrence is independent of the time since the last occurrence
3. 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?

1. The event is a car passing by, which happens at an average rate of 5 occurrences per time interval (a minute)
2. Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
3. 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

(1)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \operatorname{poissonpdf}(\lambda,k) = \frac{e^{-\lambda}\lambda^k}{k!} \end{align}

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