FRM Part I · FRM Exam Part I · Random Variables
A continuous random variable has density f(x) = 1/10 for 0 ≤ x ≤ 10, and zero otherwise. Which statement is correct?
The correct statement is that P(X = 4) is zero and P(3 ≤ X ≤ 5) is 0.20. A density value is not a point probability, and probability over an interval is density times width, 2 × 0.1, with endpoints irrelevant.
- Af(4) equals the probability that X is exactly 4, which is 0.10
- BP(X = 4) = 0 and P(3 ≤ X ≤ 5) = 0.20Correct
- CP(X = 4) = 0 and P(3 ≤ X ≤ 5) = 0.10
- DP(3 ≤ X ≤ 5) = 0.20 only if the endpoints are excluded
Explanation
For a continuous variable the probability at a single point is zero; the density value is not a probability. P(3 ≤ X ≤ 5) = (5 - 3)/10 = 0.20. Endpoints have zero probability so including or excluding them changes nothing. Option 3 uses width 1 instead of 2.
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