tõenäosustihedusfunktsioonid

Tõenäosustihedusfunktsioonid, also known as probability density functions (PDFs), are fundamental concepts in probability theory and statistics. They describe the likelihood of a continuous random variable taking on a particular value. Unlike probability mass functions, which are used for discrete random variables, PDFs are used for continuous random variables.

A PDF, denoted as f(x), must satisfy two conditions: it must be non-negative for all x, and its integral over the entire range of x must equal 1. This ensures that the total probability is 1. The probability that a continuous random variable X falls within a certain interval [a, b] is given by the integral of the PDF over that interval, i.e., P(a ≤ X ≤ b) = ∫ from a to b f(x) dx.

Common examples of PDFs include the normal distribution, the exponential distribution, and the uniform distribution. Each of these distributions has its own PDF, which describes the shape of the distribution. For instance, the normal distribution has a bell-shaped curve, while the exponential distribution has a decreasing curve.

PDFs are widely used in various fields, including physics, engineering, economics, and finance. They provide a mathematical framework for understanding and modeling random phenomena. By using PDFs, researchers and practitioners can make predictions, estimate parameters, and test hypotheses about continuous random variables.