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
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.
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):
Originally Posted by bigb
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).