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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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 | |||
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 22:00, 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?