Valószínségszámítás

Valószínűségszámítás is the Hungarian term for probability theory, a branch of mathematics concerned with the analysis of random phenomena. It deals with the mathematical formulation of uncertainty and the quantification of likelihood. The fundamental concept in valószínűségszámítás is the event, which represents an outcome of a random experiment. These events can be simple, such as a single coin toss landing heads, or complex, involving multiple conditions.

The core of valószínűségszámítás lies in assigning numerical values to the likelihood of these events occurring. This is done through probabilities, which are numbers between 0 and 1, inclusive. A probability of 0 indicates an impossible event, while a probability of 1 signifies a certain event. Probabilities are often determined through theoretical calculations based on the properties of the experiment or through empirical observation and statistical analysis.

Key concepts within valószínűségszámítás include random variables, which are functions that assign a numerical value to each outcome of a random experiment. Probability distributions describe how likely these random variables are to take on different values. The theory also explores concepts like conditional probability, which measures the likelihood of an event given that another event has already occurred, and independence, where the occurrence of one event does not affect the probability of another. Valószínűségszámítás has broad applications in fields such as statistics, physics, engineering, finance, and computer science.