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The following table gives the anticipated one-year rates of return from a certain investment and their associated probabilities.

Rate of Return
X, % Probability,
Pi
-20 0.10
-10 0.15
10 0.45
25 0.25
30 0.05

a) Calculate the expected rate of return, E(X).

b) Calculate the Variance and the Standard deviation of the returns.

c) What's the probability for this investment to yield a return of less than 10 %?

d) What's the probability for the returns of this investment to be between at least 10 % and at most 25 %?

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Solution Summary

The solution calculates the expected rate of return, E(X).

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Please see the attached file.

a) Calculate the expected rate of return, E(X).
The expected value of the return rates is the sum of the products of each return with its probability:

E(X) = (0.1) * (-20) + (0.15) * (-10) + (0.45) * 10 + (0.25) * 25 + (0.05) * 30

...

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Umut Oltulu, MBA
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  • BSc, Dokuz Eylul University
  • MBA, Texas A&M University-Kingsville
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