FRM Part I · FRM Exam Part I · Sample Moments
An analyst has i.i.d. observations with a true standard deviation of 10%. She wants the standard error of the sample mean to be one-third of what it is with 25 observations. How many observations are needed?
She needs 225 observations. Standard error falls with the square root of n, so cutting it to one-third requires n to rise by a factor of nine, from 25 to 225. Tripling the sample to 75 would reduce the error only by about 42%.
- A75
- B225Correct
- C50
- D100
Explanation
Standard error with 25 observations is 10%/5 = 2%. Target is 2%/3. Need 10%/sqrt(n) = 2%/3, so sqrt(n) = 15 and n = 225. Choosing 75 wrongly scales n linearly by 3.
Did you get it right without looking?
One question tells you little. A timed set on Sample Moments shows your real accuracy, how long you take and where you lose marks.
More Sample Moments questions
- Observations X1, X2, X3 are i.i.d. with mean mu and variance 36. Estimator A is the sample mean (X1+X2+X3)/3. Estimator B is (X1 + 2*X2 + 3*…
- An analyst records five monthly returns (in %): 2, 4, 6, 8, 10. She wants an estimate of the variance of the underlying return distribution …
- A sample of 5 returns (in %) is: 2, 4, 4, 4, 6. Its sample skewness, defined as the average cubed deviation divided by the cube of the stand…
- Observations X1, X2, X3, X4 are i.i.d. with mean mu and variance 20. An analyst uses the estimator (X1 + X2 + X3 + X4)/4 for mu. What is the…
- A risk manager estimates the mean of daily returns using n i.i.d. observations with standard deviation 1.5%. She wants the standard error of…
- A risk analyst has five daily returns (in %): 1, 3, 5, 7, 9. She treats them as a sample from a larger return distribution. What is the unbi…