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Math Help - Poisson distribution

  1. #1
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    Poisson distribution

    A guy has a chicken that gives him 10 egg/month it is known that if the eggs are not sold within a month they are no longer in good conditions to be sold. If the number of people that wants eggs per month follows a poisson distribution with mean 8 and if the guy has a profit of 7 euros for selling an egg and loses 3 if he doesn't sell if whats the expected profit per month?

    How can I get the right answer? I multiplied the mean number of people that try to buy eggs by the profit of selling that amount and I got the right answer but I dont think thats a valid way of doing it or is it?
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  2. #2
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    Quote Originally Posted by Mppl View Post
    A guy has a chicken that gives him 10 egg/month it is known that if the eggs are not sold within a month they are no longer in good conditions to be sold. If the number of people that wants eggs per month follows a poisson distribution with mean 8 and if the guy has a profit of 7 euros for selling an egg and loses 3 if he doesn't sell if whats the expected profit per month?

    How can I get the right answer? I multiplied the mean number of people that try to buy eggs by the profit of selling that amount and I got the right answer but I dont think thats a valid way of doing it or is it?
    The expected profit is (this probably can be simplified somewhat):

     \displaystyle \left[\sum_{n=0}^{10} [7 \times n-3\times (10-n)]  \times p(n,8)\right]+\left[7\times \sum_{n=11}^{\infty}p(n,8)\right]

    where p(n,8) denotes the probability of $$n from a Poission distribution with mean $$8.

    CB
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  3. #3
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    if you could repost it but this time with no code I would be very gratefull man since I cant see what's in there the way you wrote it
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