Joint Distribution

What are Joint Distribution, Moment, and Variation?

Joint Distribution

Joint distribution is based on joint probability, which can be simply defined as the probability of two events (variables) happening together. These two events are usually coined event A and event B, and can formally be written as:

p(A and B)

Joint distribution, or joint probability distribution, shows the probability distribution for two or more random variables. Hence: 

f(x,y) = P(X = x, Y = y)

The reason we use joint distribution is to look for a relationship between two of our random variables. Here, we look at two coins that both have roughly a 50/50 chance of landing on either heads (X) or tails (Y). 


XY
X25%
25%
Y25%
25%


You can use the chart to determine the probability of a certain event happening by looking at where the two events intersect. Here's another example of a joint distribution table: 

Source

Application in Machine Learning

The design of learning algorithms is such that they often depend on probabilistic assumption of the data. Uncertainty is a key concept in pattern recognition, which is in turn essential in machine learning. Being able to make optimal predictions from an incomplete data set by using the data a machine does have is essential in the framework of “smarter” and faster AI.