CDF meaning in Maths ?

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} , evaluated at x {\displaystyle x} , is the probability that X {\displaystyle X} will take a value less than or equal to x {\displaystyle x} .

Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an upwards continuous monotonic increasing cumulative distribution function F : R → [ 0 , 1 ] {\displaystyle F:\mathbb {R} \rightarrow [0,1]} satisfying lim x → − ∞ F ( x ) = 0 {\displaystyle \lim _{x\rightarrow -\infty }F(x)=0} and lim x → ∞ F ( x ) = 1 {\displaystyle \lim _{x\rightarrow \infty }F(x)=1} .

In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x {\displaystyle reference