"Linda" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> I have 1000 observations of 2 RVs from an experiments. X is the
> independent variable and Y is the dependent variable. How do I perform
> the test whether the following statement is true or not??
>
> f(X,Y)=f(X)f(Y)
>
>
> Linda
f(X,Y)=f(X)f(Y) if and only if X and Y are independent, if they are
independent they are also unrelated, so if the correlation coefficient is
not equal (or at least not not "very near") to zero then the statement is
not true.
However if the correlation coefficient is zero the statement can be false,
unless X and Y are normal, hence you can do a scatter plot, if you see a
pattern the variables are not independent.
For example if X is a variable with simmetrically distributed around zero,
that implies E(X)=0, and Y=X^(2n) , n>0, say Y=X^2, then:
E(X)E(Y)=0, because E(X) = 0
E(XY)=E(X^3)=0
and then X and Y are unrelated but much dependent.
Independence means:
E(g(X)h(Y))=E(g(X))E(h(Y)) for every function g and h where the integrals
exist, it is a strong condition.
There are also softwares that automatically try to find patterns between
samples of two variables and if they did not send a warning of a probable
indipendence.
That's all, I hope someone else gives to you a more precise answer.
Bruno
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