Cumulative distribution function: Difference between revisions

→‎Properties: + property
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# <math>0\leq F_{X_1 \ldots X_n}(x_1,\ldots,x_n)\leq 1,</math>
# <math>\lim_{x_1,\ldots,x_n \rightarrow+\infty}F_{X_1 \ldots X_n}(x_1,\ldots,x_n)=1 \text{ and } \lim_{x_i\rightarrow-\infty}F_{X_1 \ldots X_n}(x_1,\ldots,x_n)=0, \text{for all } i.</math>
 
The probability that a point belongs to a [[hyperrectangle]] is analogous to the 1-dimensional case:<ref>[http://web.archive.org/web/20160222051842/www.math.wustl.edu/~hgan/Prob2014/slides.259-327.pdf]</ref>
:<math>F_{X_1,X_2}(a, c) + F_{X_1,X_2}(b, d) - F_{X_1,X_2}(a, d) - F_{X_1,X_2}(b, c) = \operatorname{P}(a < X_1 \leq b, c < X_2 \leq d) = \int ...</math>
 
==Complex case==
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