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# Poisson Distribution Question watch

1. Hi

I have a question on the Poisson distribution that I am a bit stuck on. Any help on the method of such a question would be great

A take away restaurant has 2 incoming phone lines, A and B. The number of incoming calls in a 15 minute period on both lines are independent Poisson variates with means 4 and 5 respectively. Find the probability that in a 15 minute period:
a) More than 3 calls come in on line A
b) Less than 5 calls come in on line B
c) Exactly 9 calls come in to the restaurant.

I have done parts a and b without any bother, but am not sure about the method for part c. I was thinking I may have to find the probabilities of each way of making a total of 9 calls (i.e. 0 and 9, 1 and 8, etc.), and multiply them (i.e. P(a=0)*P(B=9), before adding all of them together???

I was thinking I may have to find the probabilities of each way of making a total of 9 calls (i.e. 0 and 9, 1 and 8, etc.), and multiply them (i.e. P(a=0)*P(B=9), before adding all of them together???

Yep.

A quick way to do it is to say that and . Then the product is just so the overall probability for the question is just
3. (Original post by RDKGames)
Yep.

A quick way to do it is to say that and . Then the product is just so the overall probability for the question is just
Thanks so much! That was really helpful
Thanks so much! That was really helpful
Alternatively, note that if and then due to them being independent, which provides the quickest way to do this question.
5. ...or, the even quicker method is to form a new variable (A + B) with Poisson distribution and lambda = 9. You are allowed to do this as the question states that A and B are independent.

Overlapped with RDKGames
6. (Original post by old_engineer)
...or, the even quicker method is to form a new variable (A + B) with Poisson distribution and lambda = 9. You are allowed to do this as the question states that A and B are independent.

Overlapped with RDKGames
(Original post by RDKGames)
Alternatively, note that if and then due to them being independent, which provides the quickest way to do this question.
Thank you both

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Updated: February 10, 2018
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