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Math Help - Simple poisson question

  1. #1
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    Simple poisson question

    Been a while since i dealt with poisson distribution any help is appreciated =]

    X~Po (5)


    Find probability that
    i) exactly 6 are sold in a randomly chosen week
    ii) exactly 6 are sold in each of 3 randomly chosen weeks
    iii) exactly 18 are sold in a randomly chosen 3 week period


    ok for i I use the formula (e^-λ8λ^X) / X!

    which gives me (e^-5 8 5^6) / 6!

    = 0.1462 (4 d.p.)

    now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

    really cant remember how to do part iii
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  2. #2
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    Quote Originally Posted by djmccabie View Post
    Been a while since i dealt with poisson distribution any help is appreciated =]

    X~Po (5)


    Find probability that
    i) exactly 6 are sold in a randomly chosen week
    ii) exactly 6 are sold in each of 3 randomly chosen weeks
    iii) exactly 18 are sold in a randomly chosen 3 week period


    ok for i I use the formula (e^-λ8λ^X) / X!

    which gives me (e^-5 8 5^6) / 6!

    = 0.1462 (4 d.p.)

    now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

    really cant remember how to do part iii
    Please define the distribution better. What exactly is X? And what is the mean of X?
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  3. #3
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    OK the bit from the beginning i missed out is

    "The number of batteries sold per week by a garage may be assumed to have a Poisson distribution with a mean 5."

    I just replace this with X~Po(5)
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  4. #4
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    Quote Originally Posted by djmccabie View Post
    Been a while since i dealt with poisson distribution any help is appreciated =]

    X~Po (5)


    Find probability that
    i) exactly 6 are sold in a randomly chosen week
    ii) exactly 6 are sold in each of 3 randomly chosen weeks
    iii) exactly 18 are sold in a randomly chosen 3 week period


    ok for i I use the formula (e^-λ8λ^X) / X!

    which gives me (e^-5 8 5^6) / 6!

    = 0.1462 (4 d.p.)

    now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

    really cant remember how to do part iii
    ii. looks fine.

    For free, let Y be the random variable number of batteries sold in a three week period. Then Y ~ Po(15). Calculate Pr(Y = 18).
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