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, ${\frac {\delta }{\delta x}}F_{X}(x)=f_{X}(x)\,$