poisson probability

• Mar 12th 2009, 02:32 PM
bigb
poisson probability
A fisherman catches fish at a poisson rate of two per hour from a large lake with lots of fish. Yesterday, he went fishing at 10:00am and caught just one fish by 10:30am and a total of three by noon. What is the probability that he can duplicate this feat tomorrow?

I think lambda is equal to 4 so the formula f(x)=3^x*e^-3/(3!) but that I dont know what to do from here? Any help would be grateful
• Mar 12th 2009, 07:32 PM
bob000
If your counting in hours lambda is 2
Remember he caught exactly 1 fish in the first 30 minutes and then exactly 2 in the next 1:30. The odds of the first event are e^-1 The odds of the second are 4.5*e^-3. Poisson problems are tricky. You have to think carefully about how to translate the word problem into a conditional. Here there is a restriction on how he catches those 3 fish so it is not the same as just asking the odds of 3 fish in 2 hours.
• Mar 12th 2009, 09:20 PM
mr fantastic
Quote:

Originally Posted by bigb
A fisherman catches fish at a poisson rate of two per hour from a large lake with lots of fish. Yesterday, he went fishing at 10:00am and caught just one fish by 10:30am and a total of three by noon. What is the probability that he can duplicate this feat tomorrow?

I think lambda is equal to 4 so the formula f(x)=3^x*e^-3/(3!) but that I dont know what to do from here? Any help would be grateful

Just to expand upon previous the remarks (I'd earlier subscribed to this thread and was planning to post later when I had time anyway):

Let X be the random variable number of fish caught in the first half an hour. X ~ Poisson(mean = 1).

Let Y be the random variable number of fish caught in the next hour and a half. Y ~ Poisson(mean = 3).

Calculate Pr(X = 1) times Pr(Y = 2).