PRB-01

Standard normal φ

pdf.

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ProbabilityGaussian

Governing equation

\\varphi(z)=e^{-z^2/2}/\\sqrt{2\\pi}

where

z: z (—)
\varphi: φ (—)

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-01 — Standard normal φ) is the form associated with Gaussian. Working symbols: $z$ $\rightarrow$ $\varphi$ . pdf.

Purpose

Purpose: compute

\varphi

from

z

in Probability & statistics via

\\varphi(z)=e^{-z^2/2}/\\sqrt{2\\pi}

pdf. 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

z = 0.000\,\mathrm{—}

, the governing relation

\\varphi(z)=e^{-z^2/2}/\\sqrt{2\\pi}

yields

\varphi = 0.39894\,\mathrm{—}

. pdf. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

z z0 —

Outputs

φ \varphi0.39894 —

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Narration of this film

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