PRB-04

Poisson P(k)

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ProbabilityPoisson

Governing equation

P(k)=e^{-\\lambda}\\lambda^k/k!

where

\lambda: λ (—)
k: k (—)
P: P (—)

Lecture brief

Historical brief

Bernoulli trials, Poisson, Gauss, Bayes and Shannon entropy turned chance into a calculus of belief and noise. The lab computes likelihood, interval and information in SI-free counts. This sheet (PRB-04 — Poisson P(k)) is the form associated with Poisson. Working symbols: $\lambda$ , $k$ $\rightarrow$ $P$ . Counts.

Purpose

Purpose: compute

P

from

\lambda

k

in Probability & statistics via

P(k)=e^{-\\lambda}\\lambda^k/k!

Counts. Use it when a real probability & statistics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\lambda = 3.000\,\mathrm{—}

k = 3.000\,\mathrm{—}

, the governing relation

P(k)=e^{-\\lambda}\\lambda^k/k!

yields

P = 0.22404\,\mathrm{—}

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Calculator

Inputs

λ \lambda3 —k k3 —

Outputs

P P0.22404 —

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