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Math Help - Poisson probability distribution Question....Stuck!

  1. #1
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    Poisson probability distribution Question....Stuck!

    Hey would really, really appreciate some help with this question on poisson distribution, this is like the only thing on my stats module so far I cant seem to understand. Lol, it just won't seem to click.


    Q:
    Estimate the number of serious road accidents a company can expect during mining operations. They know the average number of accidents on this type of mining site is .5 and follows a poisson distribution.

    Calculate the probability that
    (i) less than 2 accidents on site A
    (ii) more than 4 accidents on site A
    (iii) 3 or more accidents in total on all 3 sites

    So, is it something like this?
    Less than 2 accidents, P(X<2) = P(0)+P(1)
    I am confused
    Thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    X=number of accidents.

    P(X=x)={e^{-.5}(.5)^x\over x!} where x=0,1,2,3....

    Yes, (a) is P(X<2) = P(X=0)+P(X=1)

    (b) P(X>4)=1-[P(X=0)+...+P(X=4)]

    In (c) I assume we are talking about 3 indep sites all Poisson with mean .5.
    The sum of indep Poisson's is a Poisson.

    P(Y=y)={e^{-1.5}(1.5)^y\over y!} where y=0,1,2,3....

    and you want P(Y\ge 3)=1-P(Y\le 2)
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  3. #3
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    Quote Originally Posted by matheagle View Post

    In (c) I assume we are talking about 3 indep sites all Poisson with mean .5.
    The sum of indep Poisson's is a Poisson.
    Hey thanks so much for help. Sorry I should have mentioned site A is independent of B & C as these two are same. Is there much work involved in the solutions for these? I have been trying to do a few examples from different sites but am a bit confused as some of them seem to write the formula a different way.
    Many thanks.
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  4. #4
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    where, λ=2 and e=2.718
    e-λ = (2.718)-2 = 0.135.

    This is just from an example and while I can see the process I don't know how to go about calculating (2.718)-2,
    so how do you go about it using a calculator?
    Thanks
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  5. #5
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    Quote Originally Posted by Isildur1 View Post
    where, λ=2 and e=2.718
    e-λ = (2.718)-2 = 0.135.

    This is just from an example and while I can see the process I don't know how to go about calculating (2.718)-2,
    so how do you go about it using a calculator?
    Thanks
    It's easy,first of all if you're using a scientific calculator say... Casio fx-991ES,
    "e" is just a constant on it.
    In other words, you just press it and it allows you to raise it to any power. In your case -2, because λ=2 and e^-λ right? So your calculator should show "e^( " when you press "Shift" then "In" once each.

    Otherwise, you may key in the equivalent of "e" i.e 2.71828 and raise it to power -2 on your calculator. This should show 2.71828^(-2).

    In any case, the answer you should get is 0.1353352832.

    I really hope this helps!
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