Cumulative distribution function: Difference between revisions

(Undid revision 903217123 by (talk))
Every function with these four properties is a CDF, i.e., for every such function, a [[random variable]] can be defined such that the function is the cumulative distribution function of that random variable.
If <math>X</math> is a purely [[discrete random variable]], then it attains values <math>x_1,x_2,\ldots</math> with probability <math>p_i = \operatorname{P}(x_i)</math>, and the CDF of <math>X</math> will be [[discontinuity (mathematics)|discontinuous]] at the points <math>x_i</math> and constant in between:
:<math>F_X(x) = \operatorname{P}(X\leq x) = \sum_{x_i \leq x} \operatorname{P}(X = x_i) = \sum_{x_i \leq x} p(x_i).</math>