FRM Part I · FRM Exam Part I · Common Univariate Random Variables
The sum of 100 independent daily losses, each with mean 2 and standard deviation 3 (USD million), is approximated by a normal distribution under the CLT. What are the mean and standard deviation of the total?
The total has mean 200 and standard deviation 30. The mean of a sum is n times the individual mean, 100 times 2, while the standard deviation scales with the square root of n, so 3 times 10 equals 30. Multiplying by 100 would wrongly give 300.
- AMean 200, standard deviation 30Correct
- BMean 200, standard deviation 300
- CMean 2, standard deviation 0.3
- DMean 20, standard deviation 30
Explanation
The sum has mean 100x2=200 and variance 100x9=900, so standard deviation 30. Scaling the standard deviation by n (300) is the mistake in the second option.
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