Sannsynlighetsvektor

A sannsynlighetsvektor, also known as a probability vector, is a mathematical concept used in probability theory and statistics. It is a vector whose elements represent the probabilities of a set of mutually exclusive and collectively exhaustive events. In other words, it is a list of probabilities that sum up to 1.

The elements of a sannsynlighetsvektor are non-negative and add up to 1. This means that each element represents the likelihood of a specific event occurring, and the sum of all these likelihoods is equal to the certainty of one of the events occurring.

Sannsynlighetsvektor is often used in the context of discrete probability distributions. For example, if we have a fair six-sided die, the sannsynlighetsvektor would be [1/6, 1/6, 1/6, 1/6, 1/6, 1/6], as each face of the die has an equal probability of landing face up.

In the context of a random variable, the sannsynlighetsvektor is a list of probabilities corresponding to each possible value of the random variable. For a discrete random variable X that can take on values x1, x2, ..., xn, the sannsynlighetsvektor is [P(X=x1), P(X=x2), ..., P(X=xn)], where P(X=xi) is the probability that X equals xi.

Sannsynlighetsvektor is a fundamental concept in probability theory and is used in various applications, including statistics, machine learning, and data analysis. It provides a way to represent and manipulate probabilities in a structured and systematic manner.