PRB-03

Binomial mean

Also σ=√(npq).

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Probabilitybinomial mean

Governing equation

\\mu=np

where

n: n (—)
p: p (—)
\mu: μ (—)
\sigma: σ (—)

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-03 — Binomial mean) is the form associated with binomial mean. Working symbols: $n$ , $p$ $\rightarrow$ $\mu$ , $\sigma$ . Also σ=√(npq).

Purpose

Purpose: compute

\mu

\sigma

from

n

p

in Probability & statistics via

\\mu=np

Also σ=√(npq). 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

n = 20.000\,\mathrm{—}

p = 0.300\,\mathrm{—}

, the governing relation

\\mu=np

yields

\mu = 6.000\,\mathrm{—}

\sigma = 2.049\,\mathrm{—}

. Also σ=√(npq). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

n n20 —p p0.3 —

Outputs

μ \mu6.000 —
σ \sigma2.049 —

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Narration of this film

Also σ=√(npq).

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