exercise:174afd0173: 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 density function <math>f_X</math>. Show, using elementary calculus, that the function <math display="block"> \phi(a) = E((X - a)^2) </math> takes its minimum value when <math>a = \mu(X)</math>, and in...") |
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Let <math>X</math> be a random variable with density function <math>f_X</math>. Show, using elementary calculus, that the function | |||
Show, using elementary calculus, that the function | |||
<math display="block"> | <math display="block"> | ||
Latest revision as of 22:37, 14 June 2024
Let [math]X[/math] be a random variable with density function [math]f_X[/math]. Show, using elementary calculus, that the function
[[math]]
\phi(a) = E((X - a)^2)
[[/math]]
takes its minimum value when [math]a = \mu(X)[/math], and in that case [math]\phi(a) = \sigma^2(X)[/math].