An analyst has developed the following probability distribution for the rate of return for a common stock.

Scenario Probability Rate of Return
1 0.20 −16 %
2 0.40 7 %
3 0.40 14 %
a. Calculate the expected rate of return. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

b. Calculate the variance and the standard deviation of this probability distribution. (Use the percentage values for your calculations (for example 10% not 0.10). Round intermediate calculations to at least 4 decimal places. Enter your answer as a percentage rounded to 2 decimal places.)

Variance %2
Standard deviation %

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

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step-by-step explanation: