General Multidimensional Distributions
Remember that the cumulative distribution function for a vector of random variables is defined in terms of their joint probability distribution;
The joint distribution for two random variables can be extended to many random variables X1, ... Xn by adding them sequentially with the identity
where
and
(notice, that these latter identities can be useful to generate a random variable with given distribution function ); the density of the marginal distribution is
The joint cumulative distribution function is
and the conditional distribution function is accordingly
Expectation reads
suppose that h is smooth enough and for, then, by iterated integration by parts,
Read more about this topic: Joint Probability Distribution
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