How to Calculate the Standard Deviation on the following 3 investments?

Question by Shakespeare1982: How to Calculate the Standard Deviation on the following 3 investments?
Consider the following three investments:
X offers a return of $ 150 with a probability of 100%
Y offers a 50% chance of a return of $ 300 and a 50% chance of a return of $ 0
Z offers a 25% chance or a return of $ 400, a 50% chance of a return of $ 200,
and a 25% of a return of -$ 100 (a loss of $ 100).

As a measure of risk, calculate the standard deviation of each investment.


Answer
Answer by JoeyVX has std dev = 0
Var(Y) = EY^2 - (EY)^2 = 0.5*300^2 - 150^2 = 22500 so std dev = sqrt(22500) =

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