PRB-31

Markov inequality

Non-negative Markov bound.

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GoverningMarkov inequality

Governing equation

P(X\\ge a)\\le \\mu/a

$a \in \left[0.5, 40\right]$

where

mu: mu (—)
a: a (—)
b: Markov inequality (—)

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

P(X\\ge a)\\le \\mu/a

$a \in \left[0.5, 40\right]$

$a = 0.5$ $b = 8$

Along the curve

②

Domain of the variable — blue

a_{\min} = 0.5,\quad a_{\max} = 40

$a \in \left[0.5, 40\right]$

$a = 0.5$ $a = 0.5$

Along the curve

③

Response curve — green

P(X\\ge a)\\le \\mu/a

$a \in \left[0.5, 40\right]$

$a = 0.5$ $b = 8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}b}{\mathrm{d}a}

$a \in \left[0.5, 40\right]$

$a = 0.748$ $b^{\prime} = -8.025$

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-31 — Markov inequality) is the form associated with Markov inequality. Working symbols: $mu$ , $a$ $\rightarrow$ $b$ . Non-negative Markov bound. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

b

from

mu

a

in Probability & statistics via

P(X\\ge a)\\le \\mu/a

Non-negative Markov bound. 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

mu = 4.000\,\mathrm{—}

a = 10.000\,\mathrm{—}

, the governing relation

P(X\\ge a)\\le \\mu/a

yields

b = 0.400\,\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

mu mu4 —a a10 —

Outputs

Markov inequality b0.400 —

Reading speed

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Narration of this film

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

Non-negative Markov bound. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube