MathematicsProbability DistributionsA-Level

Variance of a Poisson Distribution Calculator

States that the variance of a Poisson distributed random variable is equal to its rate parameter lambda.

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Variance

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Overview

In a Poisson distribution, the variance is numerically identical to the expected value (mean). This property is a defining feature of the Poisson model and means the same parameter controls both central tendency and spread.

Symbols

Variables

Var(X) = Variance

Var(X)
Variance
Variable

Apply it well

When To Use

When to use: Apply this when you need the variance of a count modeled by a Poisson process.

Why it matters: It simplifies modeling because the same rate parameter determines both the mean and the variance.

Avoid these traps

Common Mistakes

  • Confusing the variance with the standard deviation.
  • Assuming the same relationship holds for all discrete distributions.

One free problem

Practice Problem

A radioactive source emits particles at a rate of 5 particles per second. What is the variance of the number of particles emitted per second?

Variance5

Solve for: Var(X)

Hint: For a Poisson distribution, variance equals the rate parameter.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Ross, S. M. (2014). A First Course in Probability.
  2. A-Level Mathematics: Statistics and Probability Specification.
  3. A-Level Mathematics Statistics Specification - Discrete Random Variables