tõenäosustihedusfunktsioonidega

Tõenäosustihedusfunktsioonidega is a Estonian term that translates to "with probability density functions". It refers to the use or application of probability density functions in a given context. A probability density function (PDF) is a function that describes the likelihood of a continuous random variable taking on a given value. The area under the curve of a PDF between two points represents the probability that the random variable falls within that interval. For a PDF, denoted by f(x), the total area under the curve must equal 1, meaning that the probability of the variable taking on any value within its range is 100%. Furthermore, the value of the PDF at any point x must be non-negative, i.e., f(x) >= 0 for all x. Examples of common probability density functions include the normal distribution, exponential distribution, and uniform distribution. Understanding and utilizing probability density functions is fundamental in various fields such as statistics, physics, engineering, economics, and machine learning for modeling and analyzing data, making predictions, and understanding uncertainty. The phrase "tõenäosustihedusfunktsioonidega" would typically be used in a sentence describing a method, calculation, or analysis that relies on these functions.