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Solve: Expected Mean, Variance and Standard Deviation

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In answering the following questions, it is given that the potential investment has the following range of possible outcomes and probabilities: 10% probability of a -20% return, 40% probability of a 15% return, 40% probability of a 25% return, and a 10% probability of a 50% return.

(a) Calculate the weighted mean of the probability distribution;
(b) calculate the variance of the probability distribution;
(c) Calculate the standard deviation of the probability distribution.
(d) Calculate the coefficient of variation of the probability distribution.
(e) Would another investment having a coefficient of variation of .25 appear to offer a higher return per unit of risk?

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Solution Preview

Please refer attached file for the complete solution. Expressions typed with the help of an equation writer are missing here.

a) Calculate the weighted mean of the probability distribution

Probability P Return ( R) P*R
0.1 -20% -0.02
0.4 15% 0.06
0.4 25% 0.1
0.1 50% 0.05

Solution Summary

This solution indicates the steps required to calculate the expected mean, variance, standard deviation and coefficient of variation of the given probability distribution. An Excel attachment file is provided which presents the solution in a neat manner.