what is cumulative distribution function

A cumulative distribution function (CDF) is a concept used in probability theory and statistics to describe the probability distribution of random variables. It gives the probability that a random variable will take a value less than or equal to a specified value. The CDF can be defined for any kind of random variable, including discrete, continuous, and mixed variables. It is represented as F(x) and is calculated as the probability that the random variable X will take a value less than or equal to x. The CDF is a fundamental tool in statistical analysis and is used to derive simple statistical properties and to analyze the frequency of occurrence of values for a given phenomenon. It is also used to create CDF plots and is implemented in various programming languages such as Python.