# Poisson Distribution question

• Jun 26th 2010, 09:43 AM
oldguynewstudent
Poisson Distribution question
Can someone help me with part c?

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of five per hour.

a) What is the probability that exactly four arrivals occur during a particular hour?

P(X=4)=$\displaystyle \frac{e^{-5}*5^{4}}{4!}$ = .17547

b) What is the probability that at least four people arrive during a particular hour?

1 - P(X=3) - P(X=2) - P(X=1) - P(X=0) = 1 - .14037 - .08422 - .03369 - .00674 = .73498

c) How many people do you expect to arrive during a 45-minute period?

$\displaystyle \lambda=\alpha t$, if $\displaystyle \alpha$=5/hr and t = 3/4 hr we get 15/4. Do we take the floor, round up if > .5, or take the ceiling? I can't find the answer in my notes, or in the text.
• Jun 26th 2010, 09:45 AM
SpringFan25
The parameter of a poisson distribution can be any (nonnegative) real number. You shouldn't be rounding it at all.

edit
Oh, now i see what you meant. You should not be rounding the expectation either, it is entirely possible for the expected value of a distribution to be an unachievable figure (eg, bournoulli variables)
• Jun 26th 2010, 09:48 AM
oldguynewstudent
Quote:

Originally Posted by SpringFan25
The parameter of a poisson distribution can be any (nonnegative) real number. You shouldn't be rounding it at all.

I'm sorry, the question is how many people do you expect to arrive during a 45-minute period? I don't think anyone wants 3 and 3/4 people showing up, not even if they're munchkins!
• Jun 26th 2010, 09:49 AM
SpringFan25
indeed i edited my post while you were typing that :P