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Car accidents at a certain intersection are randomly distributed in time according to a Poisson process,...

Car accidents at a certain intersection are randomly distributed in time according to a Poisson process, with 5 accidents per week on average. What is the probability that there are 1 accidents in the first 1 week period and 1 more in the second 1 week period.? (4 decimal accuracy please)

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Answer #1

Let X be the number of accidents in a week

X follow Poisson distribution with

the probability mass function of X is

, x= 0,1,2,....

Probability of 1 accident in a week is

Probability of 1 accident in first week and 1 more accident in the second week is

= P( X=1) *P( X=1)    ( as accidents happening each week independent of each other)

= 0.03368973*0.03368973

= 0.0011

Answer : Probability = 0.0011

P(X=1) *P(X=1) =

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