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

Read more about this topic:  Cumulative Distribution Function

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