Joint random variables are two or more random variables that are associated with the same probability space. They are often used to model the relationship between two or more variables in a system.
Individual random variables represent the outcomes of a single random experiment, while joint random variables represent the outcomes of multiple random experiments. In other words, joint random variables take into account the relationship between two or more variables, while individual random variables do not.
A joint probability distribution is a function that assigns probabilities to all possible combinations of values of two or more random variables. It describes the likelihood of specific outcomes occurring for each of the random variables simultaneously.
The joint probability of two random variables can be calculated by multiplying the individual probabilities of each variable. For example, if X and Y are two random variables, the joint probability P(X,Y) = P(X)*P(Y).
A joint probability distribution gives the probabilities of specific combinations of values of two or more random variables, while a joint cumulative distribution function gives the probability that the values of the random variables are less than or equal to a certain value. In other words, the joint cumulative distribution function provides a cumulative view of the joint probability distribution.