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Thread: Poussin distraction

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    Poussin distraction




    Poisson distribution




    Hi guys this question has mind blanked me

    A call centre receives an average of 10 calls per hour. What is the probability that the next call will occur at least 5 minutes from now?

    Do I need to find the means as 10/12 =.8333 and ten do the poussin distribution for 0 1 2 3 4 and 5

    Any help will be greatly appreciated

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    Re: Poussin distraction

    Assuming the calls follow a Poisson process as indicated. Then the occurence time of next call follows an exponential distribution.

    More specifically, if the increment of a (homogeneous) Poisson process within a time interval of length t follows a Poisson distribution with mean \lambda t, then the inter-arrival time follows an exponential distribution with mean \frac {1} {\lambda} (with the same time unit as t defined)

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    Re: Poussin distraction

    Why did you 'delete' your old post when this is the *exact* same question?

    You correctly have that the distribution of the number of calls in the next 5 minutes will follow a Poisson(10/12) distribution. If the next calls occurs 'at least 5 minutes from now' that means that there must be 0 calls in the next 5 minutes.

    BGM's answer is why I mentioned in the previous thread that there is more than one way to do this.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Poussin distraction

    Oh Dason's comment recall my memory. I just overlook the problem as it does not require the knowledge about Poisson process - simply knowing there is no arrival in the time interval is enough.

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    Re: Poussin distraction

    Quote Originally Posted by BGM View Post
    Oh Dason's comment recall my memory. I just overlook the problem as it does not require the knowledge about Poisson process - simply knowing there is no arrival in the time interval is enough.
    I like these types of problems because there typically are multiple ways to do them. I find that my students hate these types of problems for that same exact reason.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Poussin distraction

    I asked my lecturer and he said we definitely need to use the poisson distribution! Should I used .83333 and apply this for time intervals 0 1 2 3 4 and 5, because when I do so it gives me a probability nearly at 1, does that senright

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    Re: Poussin distraction


    Quote Originally Posted by Dason View Post
    You correctly have that the distribution of the number of calls in the next 5 minutes will follow a Poisson(10/12) distribution. If the next calls occurs 'at least 5 minutes from now' that means that there must be 0 calls in the next 5 minutes.
    Notice the last line. Notice how it doesn't mention any other values you would need to calculate the probability for other than 0.
    I don't have emotions and sometimes that makes me very sad.

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