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

A daily operational loss estimate L is modeled as uniform on [0, 80] (in USD thousands). What is the probability that L lies between 25 and 65, and what is P(L > 65)?

The probability of a loss between 25 and 65 is 0.50 and the probability of exceeding 65 is 0.1875. With a uniform density of 1/80, probability equals interval length divided by 80: 40/80 and 15/80.

  1. AP(25<L<65) = 0.50; P(L>65) = 0.1875Correct
  2. BP(25<L<65) = 0.50; P(L>65) = 0.8125
  3. CP(25<L<65) = 0.40; P(L>65) = 0.1875
  4. DP(25<L<65) = 0.5625; P(L>65) = 0.1875

Explanation

The density is 1/80. P(25<L<65) = 40/80 = 0.50. P(L>65) = (80-65)/80 = 15/80 = 0.1875. The 0.8125 option is P(L<65), the complement.

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