PRB-28

Normal MLE σ

MLE with n (not n-1).

Reading speed

GoverningNormal MLE σ

Governing equation

\\hat\\sigma=\\sqrt{\\sum (x_i-\\bar x)^2/n}

where

ss: ss (—)
n: n (—)
sig: Normal MLE σ (—)

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-28 — Normal MLE σ) is the form associated with Normal MLE σ. Working symbols: $ss$ , $n$ $\rightarrow$ $sig$ . MLE with n (not n-1). Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

sig

from

ss

n

in Probability & statistics via

\\hat\\sigma=\\sqrt{\\sum (x_i-\\bar x)^2/n}

MLE with n (not n-1). 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

ss = 12.000\,\mathrm{—}

n = 8.000\,\mathrm{—}

, the governing relation

\\hat\\sigma=\\sqrt{\\sum (x_i-\\bar x)^2/n}

yields

sig = 1.225\,\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

ss ss12 —n n8 —

Outputs

Normal MLE σ sig1.225 —

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.

MLE with n (not n-1). Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube