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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk analyst models daily P&L of a desk as independent draws from a distribution with mean 0.5 and standard deviation 4 (in USD thousands). Using the Central Limit Theorem, what is the standard deviation of the sample mean of 64 daily observations?

The standard deviation of the sample mean is 0.50. By the Central Limit Theorem, the standard error equals the population standard deviation divided by the square root of the sample size, so 4 divided by 8 gives 0.50. Dividing by n instead gives the incorrect 0.0625.

  1. A0.0625
  2. B0.50Correct
  3. C4.00
  4. D32.0

Explanation

The standard error of the sample mean is sigma divided by the square root of n: 4/sqrt(64) = 4/8 = 0.50. Option 0.0625 divides by n rather than its square root... actually 4/64 = 0.0625, which is the wrong base. Option 32 multiplies by 8 instead of dividing.

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