Two efficiency experts take independent measurements Y1

Chapter 6, Problem 94SE

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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)

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

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