IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
The time, in minutes, that a commuter waits for a suburban train in Mumbai is modelled as continuous uniform on the interval (0, 12). What is the probability that the wait exceeds 9 minutes?
The probability is 0.25. For a uniform distribution on (0,12), probability is proportional to length, so the interval from 9 to 12 has length 3 out of 12, giving one quarter.
- A0.2500Correct
- B0.7500
- C0.3333
- D0.0833
- 0.1250
Explanation
For U(0,12) the density is 1/12. P(X>9) = (12-9)/12 = 3/12 = 0.25. The option 0.75 is P(X<9), the complement.
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