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

Famous quotes containing the word case:

    A more problematic example is the parallel between the increasingly abstract and insubstantial picture of the physical universe which modern physics has given us and the popularity of abstract and non-representational forms of art and poetry. In each case the representation of reality is increasingly removed from the picture which is immediately presented to us by our senses.
    Harvey Brooks (b. 1915)