PRB-24

Chebyshev bound

Distribution-free tail.

Reading speed

GoverningChebyshev bound

Governing equation

P(|X-\\mu|\\ge k\\sigma)\\le 1/k^2

where

k: k (—)
b: Chebyshev bound (—)

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-24 — Chebyshev bound) is the form associated with Chebyshev bound. Working symbols: $k$ $\rightarrow$ $b$ . Distribution-free tail. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

b

from

k

in Probability & statistics via

P(|X-\\mu|\\ge k\\sigma)\\le 1/k^2

Distribution-free tail. 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

k = 2.000\,\mathrm{—}

, the governing relation

P(|X-\\mu|\\ge k\\sigma)\\le 1/k^2

yields

b = 0.250\,\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

k k2 —

Outputs

Chebyshev bound b0.250 —

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.

Distribution-free tail. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube