STEM Calculators

Using the Table of Poisson Probabilities

Statistics • Discrete Random Variables and Their Probability Distributions

Written by STEM Calculators Team Published Updated
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Using the Table of Poisson Probabilities

This tool builds a Poisson-probability table like those found in many statistics appendices: probabilities are rounded (typically to 4 decimals) and the table may be truncated once values round to 0.0000. You can read a probability directly (exactly x) or add table entries (at most / at least).

Table rules used here

  • Each entry is a rounded value of P(X = x) for a chosen λ.
  • Because of rounding, the column sum may be slightly different from 1.
  • If the table stops at some last x, it means probabilities beyond that point are extremely small (not impossible).

Poisson facts

Mean: μ = λ   •   Variance: σ2 = λ   •   Standard deviation: σ = √λ

Used only for labeling the result.

The table uses a step size (usually 0.1). Your λ can be snapped to the nearest column.

Smaller steps show more columns but make a wider table.

This mimics scanning left/right to find the correct λ column.

Many appendix tables use 4 decimals.

Auto-stop simulates truncated appendix tables.

The result is computed by reading or summing rounded table entries.

Ready
Choose λ and a query, then click “Build table & calculate”.

Visualization

Bars use the same rounding rule as the table. Dots show the exact value from the Poisson formula.

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Frequently Asked Questions

What does a Poisson probability table show?

A Poisson table lists rounded values of P(X = x) for different lambda columns and x rows. You read a value for exactly x or add multiple rows to form cumulative probabilities.

How do you use a Poisson table to find P(X <= k)?

You add the table entries for x = 0, 1, ..., k in the chosen lambda column. The calculator performs this sum using the same rounding rule as the displayed table.

Why do Poisson table columns sometimes not sum to 1?

Each entry is rounded independently, so the displayed column sum can be slightly above or below 1. Many tables also truncate once values round to 0.0000, omitting extremely small tail probabilities.

What does it mean when lambda is snapped to a table column?

Printed tables only include certain lambda values (for example in steps of 0.1). Snapping means your input lambda is rounded to the nearest available column so you can use the table method consistently.

What is the difference between table-rounded and exact Poisson probabilities?

Table-rounded values use the chosen decimal rounding and may be truncated, which can slightly change sums for cumulative probabilities. Exact probabilities come directly from the Poisson formula without rounding until the final display.

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