CDF stands for Cumulative Distribution Function. It is a mathematical concept used to describe the probability distribution of a random variable. The CDF of a random variable X is defined as the probability that the value of X is less than or equal to a given value x. It is denoted as F(x), where x is any specific value of X.
Mathematically, the CDF is represented as F(x) = P(X ≤ x), where P represents the probability.
The CDF provides important information about the likelihood of a random variable taking on certain values. It gives a complete overview of the probabilities associated with different values of the random variable. By evaluating the CDF for various values of x, one can determine the probability of obtaining a value less than or equal to a given value.
The CDF is often used in various fields of study, such as statistics, probability theory, and finance. It helps in understanding and analyzing data, and it can be used to calculate other statistical measures like percentiles and expected values.
The shape and characteristics of the CDF provide insights into the behavior and properties of the underlying random variable, such as its mean, variance, and skewness. Through the CDF, one can determine the probability of a variable falling within a specific range or calculate the probability associated with extreme values.
In summary, the Cumulative Distribution Function (CDF) is a fundamental tool in probability theory and statistics that describes the probability distribution of a random variable by providing the cumulative probability of obtaining a value less than or equal to a given value.
