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Math Help - [SOLVED] Poisson iid sample

  1. #1
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    [SOLVED] Poisson iid sample

    Hi,

    I have a question about going from the distribution of a single variable to an iid sample.

    As far as I can tell, if I have a r.v. that is normally distributed and a sample of iid r.v.'s, I then determine the joint distribution of the variables via the product of the densities.

    When I look at a r.v. that is Bernoulli, then the iid sample is distributed as Binomial (which still makes somewhat sense to me).

    I'm not sure how I get from a r.v. that is Poisson(l) to an iid sample that is distributed as Poisson(nl); specifically, it seems that I am looking at the summation of the r.v.'s rather than the product? Why or where am I not understanding this correctly?

    Thank you!
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  2. #2
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    Quote Originally Posted by Statistik View Post
    Hi,

    I have a question about going from the distribution of a single variable to an iid sample.

    As far as I can tell, if I have a r.v. that is normally distributed and a sample of iid r.v.'s, I then determine the joint distribution of the variables via the product of the densities.

    When I look at a r.v. that is Bernoulli, then the iid sample is distributed as Binomial (which still makes somewhat sense to me).

    I'm not sure how I get from a r.v. that is Poisson(l) to an iid sample that is distributed as Poisson(nl); specifically, it seems that I am looking at the summation of the r.v.'s rather than the product? Why or where am I not understanding this correctly?

    Thank you!
    Read this thread: http://www.mathhelpforum.com/math-he...isson-rvs.html
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  3. #3
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    iid sample

    mr fantastic -

    Thanks! I think I also realized my mistake: when I have iid variables of a sample, I am actually looking at their sum and multiply the marginal densities to get the equation for the sum. Makes total sense now - somehow missed that thought. Thanks for sending me in the right direction...
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