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Two efficiency experts take independent measurements Y1
Chapter 6, Problem 94SE(choose chapter or problem)
Two efficiency experts take independent measurements \(\mathrm{Y}_{1} \text { and } \mathrm{Y}_{2}\)on the length of time workers take to complete a certain task. Each measurement is assumed to have the density function given by
\(f(y)=\left\{\begin{array}{ll} (1 / 4) y e^{-y / 2}, & y>0 \\ 0, & \text { elsewhere } \end{array}\right.\)
Find the density function for the average \(U=(1 / 2)\left(\mathrm{Y}_{1}+\mathrm{Y}_{2}\right)\). [Hint: Use the method of
moment-generating functions.]
Equation Transcription:
{
Text Transcription:
Y1 and Y2
f(y)= {(1/4)ye^-y/2, y > 0, 0, elsewhere
U=(1/2)(Y1+Y2)
Questions & Answers
QUESTION:
Two efficiency experts take independent measurements \(\mathrm{Y}_{1} \text { and } \mathrm{Y}_{2}\)on the length of time workers take to complete a certain task. Each measurement is assumed to have the density function given by
\(f(y)=\left\{\begin{array}{ll} (1 / 4) y e^{-y / 2}, & y>0 \\ 0, & \text { elsewhere } \end{array}\right.\)
Find the density function for the average \(U=(1 / 2)\left(\mathrm{Y}_{1}+\mathrm{Y}_{2}\right)\). [Hint: Use the method of
moment-generating functions.]
Equation Transcription:
{
Text Transcription:
Y1 and Y2
f(y)= {(1/4)ye^-y/2, y > 0, 0, elsewhere
U=(1/2)(Y1+Y2)
ANSWER:
Step 1 of 4
First let's find out the moment generating function of