exercise:Afee895e05: 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> If <math>X</math> and <math>Y</math> are any two random variables, then the '' covariance'' of <math>X</math> and <math>Y</math> is defined by {\rm Cov}<math>(X,Y) = E((X - E(X))(Y - E(Y)))</math>. Note that {\rm Cov}<math>(X,X) = V(X)</math>. S...") |
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If <math>X</math> and <math>Y</math> are any two random variables, then the ''covariance'' of <math>X</math> and <math>Y</math> is defined by <math>\rm Cov(X,Y) = E((X - E(X))(Y -E(Y)))</math>. Note that <math>\rm Cov(X,X) = V(X)</math>. Show that, if <math>X</math> and | |||
<math>Y</math> are independent, then <math>\rm Cov(X,Y) = 0</math>; and show, by an example, that we can | |||
have <math>\rm Cov(X,Y) = 0</math> and <math>X</math> and <math>Y</math> not independent. | |||
covariance'' of <math>X</math> and <math>Y</math> is defined by | |||
E(Y)))</math>. Note that | |||
<math>Y</math> are independent, then | |||
have | |||
Latest revision as of 22:18, 14 June 2024
If [math]X[/math] and [math]Y[/math] are any two random variables, then the covariance of [math]X[/math] and [math]Y[/math] is defined by [math]\rm Cov(X,Y) = E((X - E(X))(Y -E(Y)))[/math]. Note that [math]\rm Cov(X,X) = V(X)[/math]. Show that, if [math]X[/math] and [math]Y[/math] are independent, then [math]\rm Cov(X,Y) = 0[/math]; and show, by an example, that we can have [math]\rm Cov(X,Y) = 0[/math] and [math]X[/math] and [math]Y[/math] not independent.