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Math Help - Poisson Distribution question

  1. #1
    Member oldguynewstudent's Avatar
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    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)= \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?

    \lambda=\alpha t, if \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.
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  2. #2
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    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)
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  3. #3
    Member oldguynewstudent's Avatar
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    Quote Originally Posted by SpringFan25 View Post
    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!
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  4. #4
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    indeed i edited my post while you were typing that :P
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