PRB-23

Uniform variance

Continuous uniform.

Reading speed

GoverningUniform variance

Governing equation

Var=(b-a)^2/12

$b \in \left[-10, 20\right]$

where

a: a (—)
b: b (—)
V: Uniform variance (—)

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

Var=(b-a)^2/12

$b \in \left[-10, 20\right]$

$b = -10$ $V = 8.333$

Along the curve

②

Domain of the variable — blue

b_{\min} = -10,\quad b_{\max} = 20

$b \in \left[-10, 20\right]$

$b = -10$ $b = -10$

Along the curve

③

Response curve — green

Var=(b-a)^2/12

$b \in \left[-10, 20\right]$

$b = -10$ $V = 8.333$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V}{\mathrm{d}b}

$b \in \left[-10, 20\right]$

$b = -9.811$ $V^{\prime} = -1.635$

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-23 — Uniform variance) is the form associated with Uniform variance. Working symbols: $a$ , $b$ $\rightarrow$ $V$ . Continuous uniform. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

V

from

a

b

in Probability & statistics via

Var=(b-a)^2/12

Continuous uniform. 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

a = 0.000\,\mathrm{—}

b = 6.000\,\mathrm{—}

, the governing relation

Var=(b-a)^2/12

yields

V = 3.000\,\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

a a0 —b b6 —

Outputs

Uniform variance V3.000 —

Reading speed

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Narration of this film

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

Continuous uniform. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube