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# Multinomial Calculator Online

The Multinomial Calculator is a powerful tool that simplifies complex calculations related to multinomial distributions. It’s specifically designed to determine the expected number of occurrences for different categories within a multinomial distribution, aiding in statistical analysis and predictions.

## Formula of Multinomial Calculator

The formula for calculating the expected value (E(Xi)) of a category within a multinomial distribution is:

E(Xi) = n * pi

Where:

• E(Xi) represents the expected number of occurrences for category ‘i’.
• ‘n’ stands for the total number of trials conducted.
• ‘pi’ denotes the probability of category ‘i’ occurring.

This formula serves as the backbone for understanding the likelihood of specific outcomes within a multinomial scenario.

## Table of General Terms and Conversions

Providing these general terms offers a helpful reference guide for users, aiding their understanding of the calculator’s functionalities.

## Example of Multinomial Calculator

Let’s consider an example to illustrate the application of the Multinomial Calculator:

Suppose you conduct 50 trials to categorize items into three different groups—A, B, and C. The probabilities of items falling into these categories are 0.4, 0.3, and 0.3, respectively. Using the Multinomial Calculator, you can determine the expected occurrences for each category as follows:

• Category A: E(XA) = 50 * 0.4 = 20 occurrences
• Category B: E(XB) = 50 * 0.3 = 15 occurrences
• Category C: E(XC) = 50 * 0.3 = 15 occurrences