exercise:A11455a67c: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>X</math> be a random variable with <math>E(X) = \mu</math> and <math>V(X) = \sigma^2</math>. Show that the function <math>f(x)</math> defined by <math display="block"> f(x) = \sum_\omega (X(\omega) - x)^2 p(\omega) </math> has its mini...") |
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Let <math>X</math> be a random variable with <math>E(X) = \mu</math> and <math>V(X) = \sigma^2</math>. Show that the function <math>f(x)</math> defined by | |||
\sigma^2</math>. Show that the function <math>f(x)</math> defined by | |||
<math display="block"> | <math display="block"> | ||
Latest revision as of 21:16, 14 June 2024
Let [math]X[/math] be a random variable with [math]E(X) = \mu[/math] and [math]V(X) = \sigma^2[/math]. Show that the function [math]f(x)[/math] defined by
[[math]]
f(x) = \sum_\omega (X(\omega) - x)^2 p(\omega)
[[/math]]
has its minimum value when [math]x = \mu[/math].