IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
A call centre in Pune receives calls that follow a Poisson distribution with mean 4 per hour. What is the probability that exactly 2 calls arrive in a given 30-minute period?
The rate for half an hour is 2 calls, so P(X=2) = e^-2 × 2²/2! = 0.2707. Using the hourly mean of 4 without scaling the time period would wrongly give 0.1465.
- A0.2707Correct
- B0.1465
- C0.1804
- D0.0902
- 0.2240
Explanation
The mean for 30 minutes is 2. P(X=2) = e^-2 × 2^2/2! = 2e^-2 = 2 × 0.135335 = 0.2707. Using the hourly mean of 4 directly gives 0.1465, which ignores the change in time period.
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