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- (i) Independence:
- If the distribution of z satisfies
- then we say that x and y are statistically independent.
- (ii) Function of Two Variables
- Suppose, rather than z---an ordered pair in
, we
consider 
in 
: a conventional function of x and y.
- Then
is also a random variable with distribution 
where
- This may perhaps be proved very prettily: it is obvious if you
just do one---say x-integral in Equation (8), and use the same
argument as already given for functions of a random variable.
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu