exercise:Afb59206e5: 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>, <math>Y</math>, and <math>Z</math> be independent random variables, each with mean <math>\mu</math> and variance <math>\sigma^2</math>. <ul><li> Find the expected value and variance of <math>S = X + Y + Z</math>. </li> <li> Fin...") |
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Let <math>X</math>, <math>Y</math>, and <math>Z</math> be independent random variables, each with mean | |||
with mean | |||
<math>\mu</math> and variance <math>\sigma^2</math>. | <math>\mu</math> and variance <math>\sigma^2</math>. | ||
<ul><li> Find the expected value and variance of <math>S = X + Y + Z</math>. | <ul style="list-style-type:lower-alpha"><li> Find the expected value and variance of <math>S = X + Y + Z</math>. | ||
</li> | </li> | ||
<li> Find the expected value and variance of <math>A = (1/3)(X + Y + Z)</math>. | <li> Find the expected value and variance of <math>A = (1/3)(X + Y + Z)</math>. | ||
Latest revision as of 22:38, 14 June 2024
Let [math]X[/math], [math]Y[/math], and [math]Z[/math] be independent random variables, each with mean [math]\mu[/math] and variance [math]\sigma^2[/math].
- Find the expected value and variance of [math]S = X + Y + Z[/math].
- Find the expected value and variance of [math]A = (1/3)(X + Y + Z)[/math].
- Find the expected value of [math]S^2[/math] and [math]A^2[/math].