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.

What is the expected number of animals (cats and dogs) that will 1 arrive between 12:00pm and 6:00pm?

What is the expected number of sick cats that will arrive during a 2 hour period?

What is the expected number of animals with fleas that will arrive during a 3 hour period?

Given that 20 animals arrived between 10:00am and 11:00am, what is the expected number of dogs who arrived, and what is the expected number of flea-ridden dogs who arrived?

Given that 20 animals arrived between 10:00am and 11:00am, what is the probability that none of them were flea-ridden cats, and what is the probability that exactly 3 of them were sick cats?

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?

Thanks

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.

What is the expected number of animals (cats and dogs) that will 1 arrive between 12:00pm and 6:00pm?

What is the expected number of sick cats that will arrive during a 2 hour period?

What is the expected number of animals with fleas that will arrive during a 3 hour period?

Given that 20 animals arrived between 10:00am and 11:00am, what is the expected number of dogs who arrived, and what is the expected number of flea-ridden dogs who arrived?

Given that 20 animals arrived between 10:00am and 11:00am, what is the probability that none of them were flea-ridden cats, and what is the probability that exactly 3 of them were sick cats?

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?

Thanks

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