Expected Value of a Funtion of a Random Variable

**donald17** · March 16th 2010, 07:28 PM

Grades on the last Economics 301 exam were not very good. Graphed, their distribution had a shape similar to the pdf

f_Y (y) = (1/5000)(100 - y), 0 <= y <= 100

As a way of "curving" the results, the professor announces that he will replace each person's grade, Y, with a new grade, g(Y), where g(Y) = 10sqrt(Y). Has the professor's strategy been successful in raising the class average above 60?

Thanks for any help!

**Anonymous1** · March 16th 2010, 09:07 PM

$E[g(y)]= \int_0^{100} y\times 10\times\sqrt{f_{Y}(y)} dy = \int_0^{100} y\times 10\times\sqrt{\frac{100 - y}{5000}} dy$

Use this to calculate:
Wolfram Mathematica Online Integrator

Is your answer $>60?$

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