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Summation notation from a multinomial distribution calculation

  1. Mar 7, 2008 #1
    Getting E[N] from the multinomial dist, where

    [tex]\frac{n!}{n_{1}!n_{2}!... n_{r}!}p^{n_{1}}_{1}}p^{n_{2}}_{2} ... p^{n_{r}}_{r} [/tex] is the pmf.

    Does this look right?

    [tex] \Sigma^{n}_{i=1}E\left[e^\left\{{\Sigma^{r}_{k=1}t_{k}N_{k}}\right\}}\right][/tex]
    [tex]=\Sigma^{n}_{i=1}\left[e^\left\{{\Sigma^{r}_{k=1}t_{k}N_{k}\right\}}} \frac{n!}{n_{1}!n_{2}!... n_{r}!}p^{n_{1}}_{1}}p^{n_{2}}_{2} ... p^{n_{r}}_{r} \right]\right\}[/tex]
    [tex]=\Sigma^{n}_{i=1}\frac{n!}{n_{1}!n_{2}!... n_{r}!}\left(p_{1}e^{t_{1}}\right)^{n_{1}}...\left(p_{r}e^{t_{r}}\right)^{n_{r}} [/tex]

    If so, where do I go from here?
     
  2. jcsd
  3. Mar 7, 2008 #2

    mathman

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    Science Advisor
    Gold Member

    The statement of the problem is very confusing. Your summation index is i, but i does not appear anywhere in the various expressions.
     
  4. Mar 8, 2008 #3

    ssd

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    And that, the index for sums over n(i) values shall run from 0.
     
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