University of Alberta Guide/STAT/222/Introduction/Notation

${\displaystyle F_{X}(x):X{\mbox{ is a random variable having }}cdf=P(X\leq x){\mbox{ for some value }}x\,}$

• This is basically stating that ${\displaystyle F_{X}(x)\,}$ is the probability that the random variable ${\displaystyle X\,}$ is less than or equal to the specified value ${\displaystyle x\,}$.

${\displaystyle f_{X}(x):X{\mbox{ is a random variable having }}pdf{\mbox{ value for a specific random value }}x\,}$

• This is basically stating that the value of ${\displaystyle f_{X}(x)\,}$ will represent the distribution or relative amount of times that the random value ${\displaystyle x\,}$ will appear when choosing a random value with the distribution of ${\displaystyle X\,}$
• Calculus gives us that ${\displaystyle {\frac {\delta }{\delta x}}F_{X}(x)=f_{X}(x)\,}$