Probability density function
Let
be a continuous random variable. The probability density function (pdf) of
is a function
![[eq1]](http://images1.statlect.com/probability_density_function__3.png)
such
that![[eq2]](http://images2.statlect.com/probability_density_function__4.png)
for
any interval
![[eq3]](http://images1.statlect.com/probability_density_function__5.png)
.
Probability density functions are discussed in more detail in the lecture entitled Random variables.
Example
Suppose a random variable
has probability density
function![[eq4]](http://images1.statlect.com/probability_density_function__7.png)
To compute the probability that
takes a value in the interval
![$\left[ 1,2\right] $](http://images1.statlect.com/probability_density_function__9.png)
you need to integrate the probability density function over that
interval:![[eq5]](http://images2.statlect.com/probability_density_function__10.png)
Related glossary entries
Related concepts can be found in the following glossary entries:
-
Joint probability density function: extends the concept to random vectors.
-
Marginal probability density function: the pdf of a subset of entries of a random vector.
-
Conditional probability density function: the pdf obtained conditioning on the realization of another random variable.
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