PRB-32

Poisson mean=λ

Poisson mean equals rate.

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GoverningPoisson mean=λ

Governing equation

E[X]=\\lambda

$lam \in \left[0.1, 20\right]$

where

lam: lam (—)
EX: Poisson mean=λ (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

E[X]=\\lambda

$lam \in \left[0.1, 20\right]$

$lam = 0.1$ $EX = 0.1$

Along the curve

②

Domain of the variable — blue

lam_{\min} = 0.1,\quad lam_{\max} = 20

$lam \in \left[0.1, 20\right]$

$lam = 0.1$ $lam = 0.1$

Along the curve

③

Response curve — green

E[X]=\\lambda

$lam \in \left[0.1, 20\right]$

$lam = 0.1$ $EX = 0.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}EX}{\mathrm{d}lam}

$lam \in \left[0.1, 20\right]$

$lam = 0.225$ $EX^{\prime} = 1$

Along the curve

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-32 — Poisson mean=λ) is the form associated with Poisson mean=λ. Working symbols: $lam$ $\rightarrow$ $EX$ . Poisson mean equals rate. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

EX

from

lam

in Probability & statistics via

E[X]=\\lambda

Poisson mean equals rate. 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

lam = 4.000\,\mathrm{—}

, the governing relation

E[X]=\\lambda

yields

EX = 4.000\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

lam lam4 —

Outputs

Poisson mean=λ EX4.000 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Poisson mean equals rate. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube