CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
For a continuous random variable with a probability density function, the probability that the variable takes exactly one specific value is most likely:
The probability of any single exact value of a continuous random variable is zero. Probability is measured as area under the density curve over an interval, and a single point has no width. The density height and the CDF measure different things.
- Aequal to the height of the density function at that value
- Bequal to zeroCorrect
- Cequal to the cumulative distribution function at that value
Explanation
For a continuous variable, probability is the area under the density curve over an interval. A single point has zero width and therefore zero area, so its probability is zero. The density height is not a probability, and the CDF gives P(X ≤ x).
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