Cumulative distribution function: Difference between revisions

→‎Properties: + property
m (Reverted edits by (talk) to last version by
(→‎Properties: + property)
# <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>[]</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==
Anonymous user