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Math Help - Possion or Binomial? (No calculations needed)

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    Possion or Binomial? (No calculations needed)

    I don't understand when to use the poisson formula instead of the binomial formula (assuming that there's only two formulae to choose from).

    Poisson:  P(X) = \frac{e^{-\lambda}\lambda^x}{X!}

    Binomial:  \binom{n}{X}p^x(1-p)^{n-X}

    The notes say that you use poisson when "you wish to count the number of times an event occurs in a given area of opportunity". But I don't have a clue what that means! So the question is when do I use poisson and when do I use binomial?

    Thanks

    Edit:
    Sorry for spelling the title wrong! I can't change it now apparently. Who knows what "possion" is....
    Last edited by StupidIdiot; May 26th 2008 at 01:28 PM. Reason: Spelt the title wrong
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    Quote Originally Posted by StupidIdiot View Post
    I don't understand when to use the poisson formula instead of the binomial formula (assuming that there's only two formulae to choose from).

    Poisson:  P(X) = \frac{e^{-\lambda}\lambda^x}{X!}

    Binomial:  \binom{n}{X}p^x(1-p)^{n-X}

    The notes say that you use poisson when "you wish to count the number of times an event occurs in a given area of opportunity". But I don't have a clue what that means! So the question is when do I use poisson and when do I use binomial?

    Thanks

    Edit:
    Sorry for spelling the title wrong! I can't change it now apparently. Who knows what "possion" is....
    I also found this very hard in the beginning. I'll give you the same advice given to me by Mr F: "Just hang in there!"

    In time you will know which distribution to use where. It sort of comes naturally after time.

    If a question makes use of the words "mean" or "average", then think Poisson.

    If a question gives you a success rate, and a number of times they want a success to occur, think Binomial.
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by StupidIdiot View Post
    I don't understand when to use the poisson formula instead of the binomial formula (assuming that there's only two formulae to choose from).
    Oh no, there are many!

    Binomial
    Negative Binomial
    Geometric
    Hypergeometric
    Poisson
    Exponential

    And these are just first year, first semester stuff...
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    Hello,

    Quote Originally Posted by janvdl View Post
    Oh no, there are many!

    Binomial
    Negative Binomial
    Geometric
    Hypergeometric
    Poisson
    Exponential

    And these are just first year, first semester stuff...
    There is also the most simple one : Bernouilli
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    There is also the most simple one : Bernouilli

    Basically the same thing as Binomial.
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    Quote Originally Posted by Moo View Post
    Hello,



    There is also the most simple one : Bernouilli
    Quote Originally Posted by janvdl View Post
    Basically the same thing as Binomial.
    I might be a noob in Probability but I know the Bernouilli is the exact same thing as the Binomial. So it is not basically the same thing, it is exactly the same thing.
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    Quote Originally Posted by ThePerfectHacker View Post
    I might be a noob in Probability but I know the Bernouilli is the exact same thing as the Binomial. So it is not basically the same thing, it is exactly the same thing.
    Well, I guess Bernoulli is a Binomial with n = 1 so in a sense it could be thought of as a special case of the Binomial. But technically I'd suggest the Binomial is a generalisation of the Bernoulli .......

    As for the noob business, I dare say that a half hour of concentrated study would see you understanding way more than I do .......
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    Quote Originally Posted by StupidIdiot View Post
    I don't understand when to use the poisson formula instead of the binomial formula (assuming that there's only two formulae to choose from).

    Poisson:  P(X) = \frac{e^{-\lambda}\lambda^x}{X!}

    Binomial:  \binom{n}{X}p^x(1-p)^{n-X}

    The notes say that you use poisson when "you wish to count the number of times an event occurs in a given area of opportunity". But I don't have a clue what that means! So the question is when do I use poisson and when do I use binomial?

    Thanks

    Edit:
    Sorry for spelling the title wrong! I can't change it now apparently. Who knows what "possion" is....
    The Poisson is a limiting case of the Binomial. See Poisson Distribution -- from Wolfram MathWorld
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    Moo
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    Well, we learnt it this way :

    Binomial is a succession of independent Bernouilli.

    I know they are very similar, but yet they do not really because of the different parameters for example And because one is for one event and the other for n events.


    In fact, we don't care, but ... well ~
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Moo View Post
    Well, we learnt it this way :

    Binomial is a succession of independent Bernouilli.

    I know they are very similar, but yet they do not really because of the different parameters for example And because one is for one event and the other for n events.


    In fact, we don't care, but ... well ~
    The only difference is the amount of events as you said yourself. It's the same thing.
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    Moo
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    Quote Originally Posted by janvdl View Post
    The only difference is the amount of events as you said yourself. It's the same thing.
    Yeah, yeah, if you want it to be
    But think of the definition of "the same" here, you can't just invert the two ~

    Don't wanna look messing up with ya, so I'll just give up;
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    Here is an example of a Poisson:

    The mean number of accidents per month at a certain intersection is 3. What is the probability that in a given month 4 accidents occur at the intersection?.

    Answer: P(4)=\frac{3^{4}e^{-3}}{4!}\approx{.168}

    Here is a binomial:

    You take a multiple choice quiz that has 5 questions with 4 possible answers. Find the probability that at least three are correct. Given all were random guesses.

    Answer: \sum_{k=3}^{5}C(5,k)(.25)^{k}(.75)^{5-k}= .088

    See the difference?. A poisson generally has the term 'mean' in it somewhere and deals with the probability of exactly x occurences in a given interval of time. Whereas, a binomial deals with the probability of x successes in n trials.
    See now?
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