Re: marginal distribution an joint distribution
- From: "David Jones" <dajxxx@xxxxxxxxx>
- Date: Mon, 30 Jan 2006 13:42:47 -0000
Shuangshuang.Zhou@xxxxxxxxx wrote:
> Hi, there is a theorem, p(x) is the integration of p(x,y) with
respect
> to y, is this always true?
> If y is a function of x, the integratioin of p(x,y) with respect to
x
> should be 1, not p(x), am I wrong?
Yes, you are wrong.
Consider the case where the variables are discrete and suppose y=f(x)
for all x: then
(i)sum_over_x { p(x,y)} =0 for any y for which there is no x such that
f(x)=y.
(ii)sum_over_x { p(x,y)} for a given y = sum of the values p(x,y) over
the x's such that f(x)= y, and hence the result is different for
different values of y.
However, if you first do sum_over_x_for_given_y, and then sum these
over y, the result is then 1.
David Jones
.
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- From: Shuangshuang . Zhou
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