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Compute Mean Profit From Probability Frequency

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Profit = m(x) = 500x^2

Where x is a random number with probability frequency of:

f(x) = 2(1-x) 0 < x < 1
0 elsewhere

Compute the mean profit:

The answer is $83.33, but I am unclear about how to arrive at that answer.

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Solution Summary

This solution helps compute mean profit and probability.