FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A risk system draws an integer uniformly at random from the discrete uniform distribution on {10, 11, 12, ..., 29} (20 equally likely values). What is the probability that the draw is greater than 22 and at most 27?
The probability is 0.25. The qualifying integers are 23, 24, 25, 26 and 27, which is five values out of 20 equally likely outcomes, giving 5/20 = 0.25. Miscounting the endpoints leads to 0.20 or 0.30.
- A0.20
- B0.25Correct
- C0.30
- D0.15
Explanation
Values greater than 22 and at most 27 are 23, 24, 25, 26, 27, which is 5 values. Each has probability 1/20, so the probability is 5/20 = 0.25. A count of 4 or 6 values gives the 0.20 or 0.30 distractors from boundary errors.
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