Cumulative Distribution Function - Multivariate Case

Multivariate Case

When dealing simultaneously with more than one random variable the joint cumulative distribution function can also be defined. For example, for a pair of random variables X,Y, the joint CDF is given by

where the right-hand side represents the probability that the random variable X takes on a value less than or equal to x and that Y takes on a value less than or equal to y.

Every multivariate CDF is:

1. Monotonically non-decreasing for each of its variables
2. Right-continuous for each of its variables.
3. and