Answer:
a. E(x) = 5.2000%
b. Variance = 122.16
Standard Deviation = 11.05
Step-by-step explanation:
Given
Scenario Probability Rate of Return
1 0.20 −16 %
2 0.40 7 %
3 0.40 14 %
a.
Expected Rate of Return = E(x)
E(x) = (-16% * 0.20) + (0.40 *7%) + (0.40 * 14%)
E(x) = -3.2% + 2.8% + 5.6%
E(x) = 5.2%
E(x) = 5.2000%
b.
Variance also known as the average of the squared differences from the Mean.
To calculate variance, start by calculating the mean, or average, of your sample. Then, subtract the mean from each data point, and square the differences. Next, add up all of the squared differences
Variance =
V = σ²= (−16 − 5.2)² * 0.20 + (7 − 5.2)² * 0.40 + (14 − 5.2)² * 0.40
V = σ² =122.16
Standard Deviation = σ = √SD
σ = √122.16
σ = 11.05124427383631
σ = 11.05 --- Approximated