1. Multinomial Distribution:
* Definition: In probability and statistics, the multinomial distribution is a generalization of the binomial distribution. It describes the probability of observing counts for each of *k* possible outcomes in *n* independent trials, where the probability of each outcome is constant across trials.
* Example: Imagine rolling a die 10 times. The multinomial distribution tells us the probability of getting specific numbers of each face (1, 2, 3, 4, 5, 6) after those 10 rolls.
2. Multinomial Logistic Regression:
* Definition: A statistical model used to predict a categorical dependent variable with more than two categories, based on a set of independent variables. It is an extension of logistic regression for multiple categories.
* Example: Predicting which category a customer will buy from (electronics, clothes, books) based on their demographics and browsing history.
3. Multinomial Theorem:
* Definition: In algebra, the multinomial theorem is a generalization of the binomial theorem. It provides a formula for expanding a sum of *k* terms raised to a power *n*.
* Example: The multinomial theorem can be used to expand expressions like (x + y + z)^3.
4. Multinomial Coefficient:
* Definition: A mathematical concept related to the multinomial theorem. It calculates the number of ways to divide *n* objects into *k* groups, where each group has a specific size.
* Example: The multinomial coefficient helps determine how many ways you can arrange 10 balls into 3 boxes, where the first box has 3 balls, the second has 5 balls, and the third has 2 balls.
It's important to consider the context to understand which meaning of "multinomial" is being used. If you provide more details about the situation, I can help you determine the most relevant definition.