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:
- Monotonically non-decreasing for each of its variables
- Right-continuous for each of its variables.
- and
Read more about this topic: Cumulative Distribution Function
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