# Poisson distribution

• Feb 2nd 2011, 04:03 AM
Mppl
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?
• Feb 2nd 2011, 04:25 AM
CaptainBlack
Quote:

Originally Posted by Mppl
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):

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

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

CB
• Feb 2nd 2011, 04:30 AM
Mppl
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