exercise:7b614bf427: 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>\mu = E(X)</math> and <math>\sigma^2 = V(X)</math>. Define <math>X^* = (X - \mu)/\sigma</math>. The random variable <math>X^*</math> is called the ''standardized random variable'' associated wi...") |
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Let <math>X</math> be a random variable with <math>\mu = E(X)</math> and <math>\sigma^2 = V(X)</math>. Define <math>X^* = (X - \mu)/\sigma</math>. The random variable <math>X^*</math> is called the ''standardized random variable'' associated with | |||
<math>\sigma^2 = V(X)</math>. Define <math>X^* = (X - \mu)/\sigma</math>. The random variable <math>X^*</math> is | |||
called the ''standardized random variable'' associated with | |||
<math>X</math>. Show that this standardized random variable has expected value 0 and variance 1. | <math>X</math>. Show that this standardized random variable has expected value 0 and variance 1. | ||
Latest revision as of 22:03, 14 June 2024
Let [math]X[/math] be a random variable with [math]\mu = E(X)[/math] and [math]\sigma^2 = V(X)[/math]. Define [math]X^* = (X - \mu)/\sigma[/math]. The random variable [math]X^*[/math] is called the standardized random variable associated with [math]X[/math]. Show that this standardized random variable has expected value 0 and variance 1.