- Thread starter mathy1991
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- Tags homework help poisson distribution sum of two poisson

Would I use a mark, say Mi = 1 if people, 0 if animals, and probability of Mi=1 equals to 0.5 so accidents to people is poisson lambdax0.5?

Note that you have 2 independent Poisson process, so you have the corresponding 2 independent exponentially distributed inter-arrival time too. Note that the arrival time of the next accident is the minimum of these two inter-arrival time (by memoryless property); i.e. it depends on which inter-arrival time is shorter. If the inter-arrival time of the animal accidents is smaller, then the next accident occur is an animal accident.

As a result, the probability that a particular accident is an accident to people is the probability that the inter-arrival time is smaller than the animal accident one.

After determine such probability you can immediately deduce the distribution.

Yes you need to calculate the probability but it is not 0.5. I can give you the idea to calculate this probability.

Note that you have 2 independent Poisson process, so you have the corresponding 2 independent exponentially distributed inter-arrival time too. Note that the arrival time of the next accident is the minimum of these two inter-arrival time (by memoryless property); i.e. it depends on which inter-arrival time is shorter. If the inter-arrival time of the animal accidents is smaller, then the next accident occur is an animal accident.

As a result, the probability that a particular accident is an accident to people is the probability that the inter-arrival time is smaller than the animal accident one.

After determine such probability you can immediately deduce the distribution.

Note that you have 2 independent Poisson process, so you have the corresponding 2 independent exponentially distributed inter-arrival time too. Note that the arrival time of the next accident is the minimum of these two inter-arrival time (by memoryless property); i.e. it depends on which inter-arrival time is shorter. If the inter-arrival time of the animal accidents is smaller, then the next accident occur is an animal accident.

As a result, the probability that a particular accident is an accident to people is the probability that the inter-arrival time is smaller than the animal accident one.

After determine such probability you can immediately deduce the distribution.