FRM Part I · FRM Exam Part I · Common Univariate Random Variables
Operational loss events at a bank arrive following a Poisson process with an average of 3 events per month. What is the probability of at most one event in a given month (nearest value)?
The probability is about 0.199. With a Poisson mean of 3, the chance of zero events is e^-3, about 0.0498, and the chance of exactly one is 3e^-3, about 0.1494. Their sum is 0.199. Using only the one-event term gives 0.149, which is incorrect.
- A0.199Correct
- B0.149
- C0.050
- D0.423
Explanation
P(0)=e^-3=0.0498 and P(1)=3e^-3=0.1494. The sum is 0.1991. The value 0.149 gives only exactly one event, omitting zero events.
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