Two efficiency experts take independent measurements Y1 and Y2 on the length of time

Chapter 6, Problem 6.94

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Two efficiency experts take independent measurements Y1 and Y2 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) = $ (1/4)yey/2, y > 0, 0, elsewhere. Find the density function for the average U = (1/2)(Y1 + Y2). [Hint: Use the method of moment-generating functions.]

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