Marginal probability density function
Let
be the
-th
component of a
continuous random vector
having joint probability density function
![[eq1]](http://images1.statlect.com/marginal_probability_density_function__5.png)
.
The probability density function of
- called marginal probability density function of
and denoted by
![[eq2]](http://images2.statlect.com/marginal_probability_density_function__8.png)
-
is obtained from the joint probability density function as
follows:![[eq3]](http://images1.statlect.com/marginal_probability_density_function__9.png)
In
other words, the marginal probability density function of
is obtained integrating the joint probability density function with respect to
all variables except
.
Marginal probability density functions are discussed in more detail in the lecture entitled Random vectors.
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