Question

After extensive research, you believe the probability distribution for next year's return on FB Inc is:

Return	Probability
10.5%	0.2
3.2%	0.3
-5.2%	0.3
14.9%	0.2

Compute the standard deviation of this return.  

Express your answer as a percentage to three decimal places (the percent sign is not essential). That is, if you compute a standard deviation of 0.12345, enter your answer as 12.345.

Answer 1

Standard deviation here would be the square root of the sum of squared deviations weighted by probability of individual values from expected value. (Sounds confusing? Worry not! Just follow the mathematical approach below).

First, calculate the expected value:

Expected Value = P1 * X1 + P2 * X2 + .... + Pn * Xn

Expected Value = 0.2 * 10.5% + 0.3 * 3.2% + 0.3 * -5.2% + 0.2 * 14.9%

Expected value = 0.0210 + 0.0096 - 0.0156 + 0.0298 = 0.0448 = 4.48%

Std deviation = 7.587%