A joint PDF is a mathematical function that describes the probability of two random variables, X and Y, occurring simultaneously within a given range.
A marginal PDF describes the probability of a single random variable occurring within a given range, while a joint PDF describes the probability of two or more random variables occurring simultaneously.
The joint PDF of X & Y is calculated by integrating the joint probability distribution function over the entire range of both random variables. This results in a two-dimensional function that represents the probability of each possible combination of X and Y values.
A joint CDF (cumulative distribution function) is the integral of the joint PDF. It represents the probability that X and Y will both be less than or equal to a given value. The joint PDF and CDF are closely related and can be used to calculate each other.
The joint PDF allows us to analyze the relationship between two or more variables and understand how they affect each other. It is commonly used in multivariate statistical analysis and is essential for understanding the probability distribution of complex data sets.