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Poisson Distribution Calculator

Compute Poisson probabilities, cumulative probabilities, and visualize the Poisson distribution with detailed step-by-step solutions!

Poisson Distribution Calculator
Compute the Poisson Probability:

Try the following examples: [Example 1] [Example 2] [Example 3]

Average Rate of Events \( \lambda \):
Number of Events \( k \):

Embed Poisson Distribution Calculator Widget

About Poisson Distribution Calculator

Welcome to our Poisson Distribution Calculator, a powerful tool designed to compute Poisson probabilities and cumulative probabilities with detailed step-by-step solutions and visualizations. This calculator is ideal for students, teachers, statisticians, and anyone working with Poisson distributions.

Features of the Poisson Distribution Calculator

Understanding the Poisson Distribution

The Poisson distribution models the number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event.

Definition

The probability of observing \( k \) events in an interval is given by the Poisson probability mass function (PMF):

\[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \]

Where:

Cumulative Distribution Function (CDF)

The cumulative probability of up to \( k \) events is calculated using the Poisson cumulative distribution function (CDF):

\[ P(X \leq k) = \sum_{i=0}^{k} \frac{e^{-\lambda} \lambda^i}{i!} \]

How to Use the Poisson Distribution Calculator

Applications of the Poisson Distribution Calculator

Our Poisson distribution calculator is especially useful for:

Why Use Our Poisson Distribution Calculator?

Calculating Poisson probabilities manually can be complex and time-consuming. Our calculator simplifies the process by providing:

Additional Resources

For more information on Poisson distribution and its applications, check out the following resources:

Reference this content, page, or tool as:

"Poisson Distribution Calculator" at https://miniwebtool.com/poisson-distribution-calculator/ from miniwebtool, https://miniwebtool.com/

by miniwebtool team. Updated: Jan 05, 2025

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