Joint probability density function
Let
be a continuous random vector. The joint probability density function of
is a function
![[eq1]](http://images1.statlect.com/joint_probability_density_function__3.png)
such
that![[eq2]](http://images2.statlect.com/joint_probability_density_function__4.png)
for
any
hyper-rectangle![[eq3]](http://images1.statlect.com/joint_probability_density_function__5.png)
In
other words, the probability that the random vector
takes a value in a given set is equal to the multiple integral of the joint
probability density function over that set.
Joint probability density functions are discussed in more detail in the lecture entitled Random vectors.
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