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Math Help - Expected Value of a Funtion of a Random Variable

  1. #1
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    Expected Value of a Funtion of a Random Variable

    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!
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  2. #2
    Super Member Anonymous1's Avatar
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    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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