Cats arrive at the vets as a Poisson process with rate 5 per hour. Dogs arrive t

Question

Cats arrive at the vets as a Poisson process with rate 5 per hour. Dogs arrive there as an independent Poisson process with rate 10 per hour. An arriving cat is sick with probability 1/2 and otherwise has fleas. An arriving dog is sick with probability 1/3 and otherwise has fleas. Given that 20 animals arrived between 10:00am and 11:00am, what is the expected amount of time (in hours) between the 4th arrival and the 6th arrival, and what is the expected time of the first arrival? Let X be the amount of time (in hours) from 9:00am until the first arrival of a sick dog. Suppose that exactly 3 animals arrived between 9:00am and 9:20am. Let Y = X if X 1 3 and Y = 1 3 otherwise. Find E[Y ] (given that exactly 3 animals arrived).

Explanation / Answer

Cats arrive at the vets as a Poisson process with rate 5 per hour. Dogs arrive there as an independent Poisson process with rate 10 per hour. An arriving cat is sick with probability 1/2 and otherwise has fleas. An arriving dog is sick with probability 1/3 and otherwise has fleas. Given that 20 animals arrived between 10:00am and 11:00am, what is the expected amount of time (in hours) between the 4th arrival and the 6th arrival, and what is the expected time of the first arrival? Let X be the amount of time (in hours) from 9:00am until the first arrival of a sick dog. Suppose that exactly 3 animals arrived between 9:00am and 9:20am. Let Y = X if X 1 3 and Y = 1 3 otherwise. Find E[Y ] (given that exactly 3 animals arrived).

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