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

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

The total area under the curve formed by will always be one, since that total area represents the probability that the random variable will be a value.

PDF for an Exponential RV

Probability density function

One way to calculate the PDF is to differentiate its CDF,