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

X is discrete uniform on the integers 1 to n. A analyst states that the variance of X is 52.25 (that is, (n^2 - 1)/12 = 52.25). What is P(X <= 8) for this X?

The probability is 8/25. The variance formula (n^2 - 1)/12 gives n close to 25 for a variance near 52, and with 25 equally likely integers, eight of them are at most 8, giving 8/25.

  1. A8/25Correct
  2. B8/24
  3. C8/26
  4. D8/30

Explanation

Solve (n^2 - 1)/12 = 52.25: n^2 - 1 = 627, so n^2 = 628, which is not a perfect square. Check the intended data: for n = 25, variance = 624/12 = 52. The given 52.25 is inconsistent, so the nearest integer consistent value is n = 25, giving P(X<=8) = 8/25.

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