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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A random variable X is discrete uniform on the integers 10, 11, 12, ..., 29 (20 equally likely values). What is P(X > 22 | X >= 15)?

The probability is 7/15. Conditioning on X at least 15 leaves 15 equally likely integers (15 to 29), and 7 of them (23 to 29) exceed 22. Using 20 as the denominator would ignore the conditioning information.

  1. A7/20
  2. B7/15Correct
  3. C6/15
  4. D7/14

Explanation

Values >= 15: 15 to 29, which is 15 values. Values > 22 within that: 23 to 29, which is 7 values. Conditional probability = 7/15. 7/20 ignores the conditioning and uses the full space. 7/14 uses a wrong count of the conditioning set.

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