PRB-31

Markov inequality

Non-negative Markov bound.

Reading speed

GoverningMarkov inequality

Governing equation

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

where

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

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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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