CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
Which statement about the continuous uniform distribution is most accurate?
The most accurate statement is that the probability of any single exact value is zero. Probability for a continuous variable is the area under the density over an interval, and a single point has no width. The uniform density is flat, not peaked at the midpoint.
- AIts mean always equals its variance
- BThe probability of any single exact value is zeroCorrect
- CIts probability density is highest at the midpoint of the range
Explanation
For any continuous distribution, probability is the area under the density, so a single point has zero area and zero probability. The uniform density is constant across the range, so it has no peak at the midpoint. The mean (a+b)/2 and variance (b−a)^2/12 are generally unequal.
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