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Math Help - Probability question

  1. #1
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    Probability question

    Hi I'm new here!

    I was looking through an old exam that I totally bombed thinking that I should be able to do it now, but I'm turning up just as clueless. Not knowing the answer is realy bugging me:

    "A particular website receives on average one hit per hour on a weekday afternoon. Let X denote the number of hits to be registered between noon and 3PM next Thursday.

    a) Find Var(X)
    b) Find P(X >=2)
    c) Let Y denote the number of hits to be registered between 3PM and 6PM next Thursday. Find Var(X + Y)
    d) Find E((X+Y)^2)

    Any help would be greatly appreciated!
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  2. #2
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    Hi Sushi2008,

    It seems reasonable to assume the number of hits per time period has a Poisson distribution, so X has a Poisson distribution with mean 3. This is also the variance.

    To find P(X >= 2), use P(X >= 2) = 1 - P(X=0) - P(X=1) and the formula for the pdf of a Poisson distribution.

    If Y also has a Poisson distribution with mean 3, then X+Y has a Poisson distribution with mean 6 (and variance 6).

    To find E[(X+Y)^2], use var(X+Y) = E[(X+Y)^2] + [E(X+Y)]^2.

    Hope this helps,
    jw
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  3. #3
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    Quote Originally Posted by sushi2008 View Post
    Hi I'm new here!

    I was looking through an old exam that I totally bombed thinking that I should be able to do it now, but I'm turning up just as clueless. Not knowing the answer is realy bugging me:

    "A particular website receives on average one hit per hour on a weekday afternoon. Let X denote the number of hits to be registered between noon and 3PM next Thursday.

    b) Find P(X >=2)

    Any help would be greatly appreciated!
    For the evaluation of Sushi's comment to check your work, go here:

    Poisson Distribution

    n = 3, p = 1, k = 1 since we want >= 2.

    Your answer should be 0.8008

    Check out the math and let me know if you have questions.
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