A driver is chosen at random from the Owl Insurance Company\'s records. His acci

Question

A driver is chosen at random from the Owl Insurance Company's records. His accident experience follows a Poisson distribution. The probability that this driver has 0 accidents during the next two months is equal to the probability that he has 1 accident during the next two months. The number of accidents in different months are mutually independent. the probability that he will have 2 accidents during the next month, the probability that he will have at least 2 accidents during the next quarter.

Explanation / Answer

Let X be no of accidents in the next two months

P(x; ) = (e-) (x) / x!

P(X=0) = P(x=1)

i.e.(e-) (0) / 0! = (e-) () / 1!

mu =1

a) P(X=2 when average =1) = 0.1839

b) P(x>=2 when average is 1.5 since 3 months) = 0.4422

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