Probability of States***********************************************************

Question

Probability of States************************************************************Investment Occurrence Returns
Economic boom 18% ****************************************************************************20%
Economic growth 42%***************************************************************************16%
Economic decline 30%*************************************************************************** 3%
Depression 10% ************************************************************************** MINUS 25%

Explanation / Answer

E(X)=mean= 0.18*0.2+0.42*0.16 +0.3*0.03 - 0.1*0.25 = 0.0872 (8.72%)

E(X^2) =0.18*0.2^2+0.42*0.16^2 +0.3*0.03^2 + 0.1*0.25^2 = 0.024472

Var(X)=E(X^2) - [E(X)]^2 = 0.024472 - 0.0872^2 = 0.01686816

Standard deviation = 0.01686816 =0.1298 (12.98%)

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