Joint cumulative distribution function

Definition:

• Cumulative distribution function for Joint Distribution
• We define Joint cumulative probability distribution function of $X$ and $Y$ by:$F(a,b)=P\{X\le a,Y\le b\}-\infty <a,b<\infty$
• All joint probability statements can be answered in terms of joint distribution function $P(a_1<X\le a_2,b_1<Y\le b_2)=F(a_2,b_2)-F(a_1,b_2)-F(a_2,b_1)+F(a_1,b_1)$

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