In probability theory and statistics, the cumulative distribution function of a real-valued random variable X, or simply the distribution function of X weighted by x, is the probability that X takes a value less than or equal to x.
The cumulative distribution function (CDF) of a random variable X is defined as FX(x)=P(X≤x) for all x∈R. Note that the subscript X indicates that this is the CDF of the random variable X. Also note that the CDF is defined for all x∈R. Let's look at an example.