Joint Probability Distribution

Joint Probability Distribution

In the study of probability, given two random variables X and Y that are defined on the same probability space, the joint distribution for X and Y defines the probability of events defined in terms of both X and Y. In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to any number of random variables, giving a multivariate distribution. The equation for joint probability is different for both dependent and independent events.

The joint probability function of a set of variables can be used to find a variety of other probability distributions. The probability density function can be found by taking a partial derivative of the joint distribution with respect to each of the variables. A marginal density ("marginal distribution" in the discrete case) is found by integrating (or summing in the discrete case) over the domain of one of the other variables in the joint distribution. A conditional probability distribution can be calculated by taking the joint density and dividing it by the marginal density of one (or more) of the variables.

Read more about Joint Probability Distribution:  Example, Cumulative Distribution, General Multidimensional Distributions, Joint Distribution For Independent Variables, Joint Distribution For Conditionally Dependent Variables

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