Summation notation from a multinomial distribution calculation

[Somefantastik]

Getting E[N] from the multinomial dist, where

$$\frac{n!}{n_{1}!n_{2}!... n_{r}!}p^{n_{1}}_{1}}p^{n_{2}}_{2} ... p^{n_{r}}_{r}$$ is the pmf.

Does this look right?

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

If so, where do I go from here?

 

[mathman]

The statement of the problem is very confusing. Your summation index is i, but i does not appear anywhere in the various expressions.

 

[ssd]

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