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FRM Part I · FRM Exam Part I · Random Variables

A random variable X has the discrete distribution P(X = 0) = 0.2, P(X = 5) = 0.5, P(X = 10) = 0.3. Which value is the median, defined as the smallest x with F(x) ≥ 0.5?

The median is 5. The CDF is 0.2 at 0 and jumps to 0.7 at 5, so 5 is the smallest value whose cumulative probability reaches at least 0.5. The value 7.5 is not in the support, and 10 is only where the CDF hits 1.

  1. A0
  2. B5Correct
  3. C7.5
  4. D10

Explanation

F(0) = 0.2, which is below 0.5. F(5) = 0.2 + 0.5 = 0.7, which is at least 0.5, and 5 is the smallest value meeting this. The value 7.5 is a midpoint of the support, not a quantile of this distribution, and 10 is the point where F reaches 1.

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