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

$F_X(x):X\text{ is a random variable having }cdf=P(X\le x)\text{ for some value }x$

• This is basically stating that $F_X(x)$ is the probability that the random variable $X$ is less than or equal to the specified value $x$.

$f_X(x):X\text{ is a random variable having }pdf\text{ value for a specific random value }x$

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