exercise:Ee0a273eda: 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> In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than <math>2^\circ</math> from <math>62^\circ</math>. The temperature is, in fact, a random variable <math>F</math> with distribution <math display="block"> P_...")
 
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<div class="d-none"><math>
In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than <math>2^\circ</math> from <math>62^\circ</math>.  The temperature is, in fact, a random variable <math>F</math> with distribution
\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> In a certain manufacturing process, the (Fahrenheit)
temperature never varies by more than <math>2^\circ</math> from <math>62^\circ</math>.  The temperature is,
in fact, a random variable <math>F</math> with distribution


<math display="block">
<math display="block">
P_F = \pmatrix{ 60 & 61 & 62 & 63 & 64 \cr 1/10 & 2/10 & 4/10 & 2/10 & 1/10 \cr}\ .
P_F = \pmatrix{ 60 & 61 & 62 & 63 & 64 \cr 1/10 & 2/10 & 4/10 & 2/10 & 1/10 \cr}\ .
</math>
</math>
<ul><li> Find <math>E(F)</math> and <math>V(F)</math>.
<ul style="list-style-type:lower-alpha"><li> Find <math>E(F)</math> and <math>V(F)</math>.
</li>
</li>
<li> Define <math>T = F - 62</math>.  Find <math>E(T)</math> and <math>V(T)</math>, and compare these answers with
<li> Define <math>T = F - 62</math>.  Find <math>E(T)</math> and <math>V(T)</math>, and compare these answers with

Latest revision as of 21:00, 14 June 2024

In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than [math]2^\circ[/math] from [math]62^\circ[/math]. The temperature is, in fact, a random variable [math]F[/math] with distribution

[[math]] P_F = \pmatrix{ 60 & 61 & 62 & 63 & 64 \cr 1/10 & 2/10 & 4/10 & 2/10 & 1/10 \cr}\ . [[/math]]

  • Find [math]E(F)[/math] and [math]V(F)[/math].
  • Define [math]T = F - 62[/math]. Find [math]E(T)[/math] and [math]V(T)[/math], and compare these answers with those in part (a).
  • It is decided to report the temperature readings on a Celsius scale, that is, [math]C = (5/9)(F - 32)[/math]. What is the expected value and variance for the readings now?