Marginal probability mass function
Let
be the
-th
component of a
discrete random vector
having joint probability mass function
![[eq1]](http://images2.statlect.com/marginal_probability_mass_function__5.png)
and support
.
The probability mass function of
- called marginal probability mass function of
and denoted by
![[eq2]](http://images2.statlect.com/marginal_probability_mass_function__9.png)
-
is obtained from the joint probability mass function as
follows:![[eq3]](http://images1.statlect.com/marginal_probability_mass_function__10.png)
where
the sum is over the
set:![[eq4]](http://images2.statlect.com/marginal_probability_mass_function__11.png)
In
other words, the marginal probability mass function of
at the point
is obtained summing the joint probability mass function over all the vectors
that belong to the support
and are such that their
-th
component is equal to
.
A more detailed discussion of the marginal probability mass function can be found in the lecture entitled Random vectors.
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