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

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

The total area under the curve formed by <math>f_{X}(x)\,</math> will always be one, since that total area represents the probability that the random variable <math>X\,</math> will '''be''' a value.

'''PDF for an Exponential RV'''

[[Image:Exponential distribution pdf.png|325px|Probability density function]]

One way to calculate the PDF is to differentiate its CDF, <math>\frac{\delta}{\delta x}F_{X}(x) = f_{X}(x)\,</math>

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