Jaotuvusfunktsioone

Jaotuvusfunktsioone, also known as distribution functions, are fundamental concepts in probability theory and statistics. A distribution function describes the probability that a random variable takes on a value less than or equal to a specific point. For a discrete random variable X, the distribution function F(x) is defined as the sum of probabilities for all values less than or equal to x. For a continuous random variable Y, the distribution function F(y) is defined as the integral of its probability density function from negative infinity up to y.

Distribution functions have several key properties. They are non-decreasing, meaning that if x1 is less than or equal to x2, then F(x1) must be less than or equal to F(x2). Additionally, the limit of the distribution function as the variable approaches negative infinity is zero, and the limit as the variable approaches positive infinity is one. These properties ensure that the function accurately represents a cumulative probability.

The concept of distribution functions is crucial for understanding and analyzing random phenomena. They allow for the calculation of probabilities of various events, such as the probability of a value falling within a certain range. Different types of random variables have specific associated distribution functions, such as the binomial distribution function for discrete events or the normal distribution function for continuous data. Understanding distribution functions is essential for statistical modeling, hypothesis testing, and making informed decisions based on data.