Getting E[N] from the multinomial dist, where(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Summation notation from a multinomial distribution calculation

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