Multinomiaalinen

Multinomiaalinen is a term used in several fields, most commonly in mathematics and statistics. In mathematics, a multinomial coefficient, often denoted as $\binom{n}{k_1, k_2, \dots, k_m}$ where $k_1 + k_2 + \dots + k_m = n$, represents the number of ways to partition a set of $n$ distinct objects into $m$ distinct subsets of specified sizes $k_1, k_2, \dots, k_m$. This is a generalization of the binomial coefficient. The formula for a multinomial coefficient is $\frac{n!}{k_1! k_2! \dots k_m!}$.

In statistics, the term refers to a multinomial distribution. This is a probability distribution that describes the outcome of $n$ independent trials, where each trial can result in one of $m$ possible outcomes, each with a fixed probability. The probabilities of each outcome must sum to 1. For example, if you roll a die multiple times, the outcome of each roll can be one of six possibilities (1 through 6), and the multinomial distribution can model the probabilities of observing a certain number of each outcome over many rolls. The multinomial distribution is a generalization of the binomial distribution, which applies when there are only two possible outcomes for each trial. The term "multinomiaalinen" itself, when used in a general context, implies having multiple parts, categories, or terms, reflecting its mathematical and statistical applications.