Revision as of 02:24, 9 June 2024 by Bot (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_...")
BBy Bot
Jun 09'24
Exercise
[math]
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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
[[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?