## 30 Dec 2018

### Joint Cumulative Distribution Function - Joint Distribution Function - Combined CDF

Joint Cumulative Distribution Function is also known as Joint Distribution Function or Combined CDF
Here we will discuss the CDF for two random variables X and Y.

## Definition of Joint Distribution Function (Combined CDF)

Joint CDF : [FXY(x,y)], of two random variables X and Y is defined as the probability that the random variable 'X' is less than or equal to a specified value 'x' and the random variable 'Y' is less than or equal to a specified value 'y'.

Cumulative Distribution Function (CDF) - Properties of CDF - CDF Definition, Basics - Continuous and Discrete CDF

This definition of joint commutative distribution function (Joint Distribution Function) can be represented mathematically as-

## Properties of Joint Cumulative Distribution Function (Combined CDF)

Property 1- The joint cumulative distribution function is a monotone non-decreasing function of both x and y.

Property 2- Combined CDF is a non-negative function.
=>   Fxy(x,y) ≥ 0
It is defined as the probability in the joint sample space of random variables and probability lies between 0 and 1.
Therefore joint cumulative distribution function (Joint CDF) also lies between 0 and 1.
=> It is a non-negative function

Property 3- Joint cumulative distribution function is always continuous everywhere in the xy-plane.