# 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):****See:**Joint Probability Function.

## 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]X[/math] and [math]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]x[/math] and*Y*(*s*) <=*y*})*F*(_{X,Y}*x,y*) =*P*(*X*≤*x*,*Y*≤*y*).