valószínségvektort

Valószínűségvektor is a Hungarian term that translates to "probability vector" in English. It is a fundamental concept in probability theory and statistics, particularly in the study of discrete probability distributions. A probability vector is essentially a vector where each element represents the probability of a specific outcome occurring.

The defining characteristics of a probability vector are that all its elements are non-negative, meaning they are zero or positive, and the sum of all its elements must equal one. This "sum to one" property is crucial because it signifies that the probabilities of all possible mutually exclusive outcomes of an event must collectively account for the entire probability space, which is always normalized to 1.

Probability vectors are commonly used to represent the probability mass function (PMF) of a discrete random variable. For instance, if we consider the outcome of rolling a fair six-sided die, the probability vector would be [1/6, 1/6, 1/6, 1/6, 1/6, 1/6]. Each element corresponds to the probability of rolling a 1, 2, 3, 4, 5, or 6, respectively. The sum of these probabilities is 1, and each individual probability is non-negative.

Beyond simple examples, probability vectors are employed in various fields such as machine learning, econometrics, and physics to model complex systems where outcomes can be categorized and their likelihoods quantified. They provide a concise and mathematical way to describe the uncertainty associated with a set of possible results.