FRM Part I · FRM Exam Part I · Random Variables
A discrete random variable X takes values 1, 2, 3 and 4 with probabilities 0.10, 0.25, 0.40 and 0.25 respectively. What is the cumulative distribution function F(3) = P(X ≤ 3)?
F(3) equals the sum of probabilities for all outcomes at or below 3: 0.10 + 0.25 + 0.40 = 0.75. The CDF accumulates probability mass up to and including the point, so it is not just the probability at 3 alone.
- A0.40
- B0.65
- C0.75Correct
- D1.00
Explanation
F(3) = P(X=1)+P(X=2)+P(X=3) = 0.10+0.25+0.40 = 0.75. The value 0.40 is only the probability mass at 3, and 0.65 is the sum of the first two plus nothing else (0.10+0.25+0.40 is not 0.65; it omits the correct accumulation). 1.00 would be F(4).
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