In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2. The numbers of tornadoes in different weeks are mutually independent.

Calculate the probability that fewer than four tornadoes occur in a three-week period.

• 0.13
• 0.15
• 0.29
• 0.43
• 0.86

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

The sum of independent Poisson variables is also Poisson, with the means added. Thus the number of tornadoes in a three week period is Poisson with a mean of 3x2 = 6. Then,

[[math]] P( N \lt 4) = p(0) + p(1) + p(2) + p(3) = e^{-6}\left( \frac{6^0}{0!} + \frac{6^1}{1!} + \frac{6^2}{2!} + \frac{6^3}{3!} + \right) = 0.1512. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.