University of Alberta Guide/STAT/222/Formulas and Functions/Probability Density Functions

The probability density function, $f_X(x)$, represents the distribution of the random variable $X$. Wikipedia defines the PDF as a smoothed out version of the random variable's histogram of its distribution. Basically, the larger the value of $f_X(x)$ for a specific value $x$ means the more often that value $x$ will appear when choosing a random variable of its type of distribution.

The total area under the curve formed by $f_X(x)$ will always be one, since that total area represents the probability that the random variable $X$ will be a value.

PDF for an Exponential RV

One way to calculate the PDF is to differentiate its CDF, $\frac{\delta }{\delta x}{F}_X(x)=f_X(x)$