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Math Help - probability

  1. #1
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    probability

    1, In a particular departmental store customers arrive at a check up counter
    according to poisson distribution at an average of 5 per hour
    During a particular 1 hour period,
    a,what is the probability that at least 3 customers will arrive
    b,What is the probability that in a given 2 hours period exactly 2 customers will arrive
    c,In a 30 minute period determine the probability that at most 2 customers will arrive
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  2. #2
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    so we know that are  \lambda = 5, so for:

    a)  P(X \geq 3) = P(X=3) \cup P(X=4) \cup P(X=5)

     P(X \geq 3) = \frac{5^3}{3!}e^{-5}+\frac{5^4}{4!}e^{-5} + \frac{5^5}{5!}e^{-5}


    b)  \lambda = 2 \times 5 = 10

     P(X =  2 ) = \frac{10^2}{2!}e^{-10}


    c)  \lambda = \frac{1}{2} \times 5 = \frac{5}{2}

     P(X \leq 2) = P(X=0) \cup P(X=1) \cup P(X=2)

     P(X \leq 2) = \frac{2.5^0}{0!}e^{-2.5}+\frac{2.5^1}{1!}e^{-2.5} + \frac{2.5^5}{2!}e^{-2.5}
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