Joint Cumulative Probability Function

A Joint Cumulative Probability Function is a joint probability function that is a cumulative distribution function.

• AKA: Joint CDF.
• Context:
  • input: two or more Continuous Random Variable Events (x,y).
  • Function Domain: two or more Random Variable(X, Y) defined on the same Continuous Sample Space (S)
  • range: the Probability of Events (-Inf,x] and (-Inf,y] Occurring.
  • range: an Event Probability.
  • …
• Counter-Example(s):
  • Marginal CDF.
• See: Joint Probability Function.

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References

1986

• (Larsen & Marx, 1986) ⇒ Richard J. Larsen, and Morris L. Marx. (1986). “An Introduction to Mathematical Statistics and Its Applications, 2nd edition." Prentice Hall
  • Definition 3.3.2. Let [math]\displaystyle{ X }[/math] and [math]\displaystyle{ Y }[/math] be two random variables defined on the same sample space S. The joint cumulative distribution function (or joint cdf) of X and Y is defined F_X,Y(x,y), where

    F_X,Y(x,y) = P({s∈S } X(s) <= [math]\displaystyle{ x }[/math] and Y(s) <= y})

    F_X,Y(x,y) = P(X≤x, Y≤y).

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