Cumulative Distribution Functions
A Cumulative Distribution Function (CDF) is a mathematical function that describes the probability that a random variable will take a value less than or equal to a specific number. It provides a complete picture of the distribution of the variable by accumulating probabilities from the lowest value up to the specified point. The CDF is useful in statistics for understanding the likelihood of different outcomes.
The CDF is defined for both discrete and continuous random variables. For discrete variables, it sums the probabilities of all outcomes up to a certain value, while for continuous variables, it integrates the probability density function (PDF) over the range. The CDF always ranges from 0 to 1, indicating the total probability.