Correct answer is 0.52508059.
Answer is not given in the options.
First we will calculate the mean. The formula for mean is:
Mean = p1 * r1 + p2 * r2 + p3 * r3
where, p1,p2 and p3 are the probabilities and r1,r2 and r3 are the returns.
Putting the given values of the probability in the above formula, we get,
Mean = (0.14 * 25%) + (0.5 * 15%) + (0.36 * 5%)
Mean = 3.5 + 7.5 + 1.8
Mean = 12.8%
Next we will calculate the standard deviation. Steps for calculating standard deviation are:
First we will calculate the deviation of returns from the mean return as per below:
Boom : 25 - 12.8 = 12.2
Normal: 15 - 12.8 = 2.2
Recession 5 - 12.8 = -7.8
In the next step, we will square the deviations computed above, as per below:
Boom: (12.2)2 = 148.84
Normal: (2.2)2 = 4.84
Recession : (-7.8)2 = 60.84
In the next step, we will multiply the squared deviations computed above with their probabilities as per below:
Boom: 148.84 * 0.14 = 20.8376
Normal growth: 4.84 * 0.5 = 2.42
Recession: 60.84 * 0.36 = 21.9024
In the next step we will add up the values calculated above to find the variance, as per below:
Variance = 20.8376 + 2.42 + 21.9024 = 45.16
In the next step, we will square root the variance calculated above to find the standard deviation:
Standard deviation = (45.16)1/2 = 6.72011904656
In the final step, we will calculate the coefficient of variation as per below:
Coefficient of variation = Standard / Mean * 100
Coefficient of variation = 6.72011904656 / 12.8
Coefficient of variation = 0.5250
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