tõenäosusfunktsioon

Tõenäosusfunktsioon, also known as a probability density function (PDF) in English, is a mathematical function that describes the likelihood of a continuous random variable taking on a specific value. It is a fundamental concept in probability theory and statistics, used to model the distribution of random variables.

The probability density function is defined for continuous random variables, unlike the probability mass function, which is used for discrete random variables. The value of the PDF at a given point does not directly represent the probability of the random variable taking that value; instead, it represents the relative likelihood of the variable being close to that value. The actual probability is found by integrating the PDF over an interval.

The PDF must satisfy two conditions: it must be non-negative for all values of the random variable, and the total area under the curve of the PDF must equal one. This ensures that the probabilities are correctly normalized.

Common examples of probability density functions include the normal distribution, the exponential distribution, and the uniform distribution. Each of these has its own unique shape and properties, but they all serve to describe the distribution of continuous random variables.

In practice, the probability density function is used in a variety of applications, including statistical modeling, risk assessment, and data analysis. It provides a way to understand the underlying distribution of data and make predictions about future observations.