denzitásfüggvény

A denzitásfüggvény, often translated as probability density function (PDF) in English, is a fundamental concept in probability theory and statistics. It describes the relative likelihood for a continuous random variable to take on a given value. Unlike discrete probability distributions where probabilities are assigned to specific outcomes, for continuous variables, the probability of any single specific value is zero. Instead, the PDF indicates the probability density over a range of values.

The value of a denzitásfüggvény at a particular point does not directly represent a probability. Instead, the probability of the random variable falling within a certain interval is found by integrating the denzitásfüggvény over that interval. Mathematically, for a continuous random variable X with PDF f(x), the probability that X lies between a and b is given by the integral of f(x) from a to b.

Key properties of a denzitásfüggvény include: non-negativity, meaning f(x) ≥ 0 for all x, and that the total area under the curve must equal one, representing the certainty that the variable will take on some value. The shape of the denzitásfüggvény graphically illustrates the distribution of the random variable, showing where values are more or less likely to occur. Common examples include the normal (Gaussian) distribution, uniform distribution, and exponential distribution, each characterized by distinct denzitásfüggvény shapes.