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

$$F_{X}(x) : X \mbox{ is a random variable having } cdf = P(X \leq x) \mbox{ for some value } x\,$$ $$f_{X}(x) : X \mbox{ is a random variable having } pdf \mbox{ value for a specific random value } x\,$$
 * 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 $$x\,$$.
 * 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 $$\frac{\delta}{\delta x}F_{X}(x) = f_{X}(x)\,$$