FRM Part I · FRM Exam Part I · Fundamentals of Probability
A continuous random variable X has probability density function f(x) = 0.5x for 0 ≤ x ≤ 2 and zero elsewhere. What is P(X > 1)?
P(X > 1) equals the integral of 0.5x from 1 to 2, which is 0.25 times (4 minus 1) = 0.75. Equivalently, P(X ≤ 1) is 0.25, so the complement is 0.75.
- A0.25
- B0.50
- C0.75Correct
- D0.60
Explanation
P(X > 1) = integral from 1 to 2 of 0.5x dx = 0.25(4 - 1) = 0.75. Check: total area is 0.25 x 4 = 1, and P(X ≤ 1) = 0.25, so the complement is 0.75. The 0.25 option is P(X ≤ 1).
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