# Summation notation from a multinomial distribution calculation

• Somefantastik
In summary, the conversation discusses the process of obtaining E[N] from the multinomial distribution, using the pmf formula given. The individual components of the formula, such as the summation index and the values of n(i), are unclear and require further clarification.
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?

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

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

## 1. What is summation notation from a multinomial distribution calculation?

Summation notation from a multinomial distribution calculation is a mathematical expression that represents the total sum of a series of numbers. In the context of a multinomial distribution, it is used to calculate the probability of a specific outcome occurring among multiple categories or groups.

## 2. How is summation notation used in a multinomial distribution calculation?

In a multinomial distribution calculation, summation notation is used to represent the probabilities of each possible outcome occurring. The notation is typically written as: Σi=1n Pi, where Σ represents the summation symbol, i=1 indicates the starting value of the index, n indicates the ending value of the index, and Pi represents the probability of outcome i.

## 3. What is a multinomial distribution?

A multinomial distribution is a probability distribution that describes the outcomes of a categorical variable with more than two categories. It is often used in situations where there are multiple possible outcomes and each outcome has a different probability of occurring.

## 4. How is a multinomial distribution different from a binomial distribution?

A binomial distribution is used to describe the outcomes of a categorical variable with two possible outcomes (such as success or failure). A multinomial distribution, on the other hand, is used to describe the outcomes of a categorical variable with more than two categories. Additionally, in a binomial distribution, the probabilities for each outcome remain the same for each trial, while in a multinomial distribution, the probabilities may vary for each outcome.

## 5. Can summation notation be used for other types of distributions?

Yes, summation notation can be used for other types of distributions, such as the normal distribution or the Poisson distribution. It is a general mathematical notation that can be applied to represent the total sum of a series of numbers in any type of distribution or mathematical calculation.

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