Question 8.10: A reinsurance company works on a premium policy for natural ......

Introduction to Statistics and Data Analysis With Exercises, Solutions and Applications in R [1403016]

A reinsurance company works on a premium policy for natural disasters. Based on experience, it is known that W = “number of natural disasters from October to March” (winter) is Poisson distributed with λ $_{W}$ = 4. Similarly, the random variable S = “number of natural disasters from April to September” (summer) is Poisson distributed with λ $_{S}$ = 3. Determine the probability that there is at least 1 disaster during both summer and winter based on the assumption that the two random variables are independent.

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P(S ≥ 1,W ≥ 1) $\overset{indep.}{=}$ P(S ≥ 1) · P(W ≥ 1)

= (1 − P(S = 0)) · (1 − P(W = 0))

$=\left(1-e^{-3}\frac{3^{0}}{0!} \right)\cdot \left(1-e^{-4}\frac{4^{0}}{0!} \right)$

≈ 0.93.

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