Statistics Solutions

(Steps Shown) Two efficiency experts take independent measurements Y_1 and Y_2 on the length of time workers take to complete a certain task. Each measurement

Question: Two efficiency experts take independent measurements \(Y_{1}\) and \(Y_{2}\) on the length of time workers take to complete a certain task. Each measurement is assumed to have the density function. given by

\[f(y)= \begin{cases}(1 / 4) y e^{-y / 2}, & y>0 \\ 0, & \text { elsewhere }\end{cases}\]

Find the density function for the average \(U=(1 / 2)\left(Y_{1}+Y_{2}\right) .\) Hint: Use the method of moment-generating functions.]

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