FRM Part I · FRM Exam Part I · Random Variables
For the CDF F(x) = x^2/16 on 0 ≤ x ≤ 4 (zero below 0, one above 4), what is the 75th percentile (quantile) of X?
The 75th percentile is about 3.46. The quantile is the x at which the CDF equals 0.75, so x^2/16 = 0.75, giving x^2 = 12 and x = √12. Taking 0.75 times 4 would wrongly treat the variable as uniform.
- A3.00
- B2.83
- C3.46Correct
- D12.00
Explanation
Solve F(q) = 0.75: q^2/16 = 0.75, so q^2 = 12 and q = √12 ≈ 3.46. Option 3.00 is 0.75 times the maximum of 4, which would hold for a uniform variable. Option 12.00 is q^2, forgetting the square root.
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