Random variable

\(\underline{cdf:}\)cumulative distribution function
\(F(x)=P(X \leq x)\)
\(\underline{pmf:}\)probability mass function(for discrete probability distribution )
(1)\(p(x) \geq0,x \in \mathcal{X}\)
(2)\(\sum\limits_{x \in \mathcal{X}}P(x)=1\)
\(\underline{pdf:}\)probability density function
(1)\(f(x) \geq 0\)for all x,
(2)\(\int_{-\infty}^{\infty}f(x)dx=1\)