Re: Dividing Random Variables

Armando wrote:
Hello,

I wish to know if it is possible to divide random variables.

For example: if I have two random variables:
-F(mu1,sigma1)
-A(mu2,sigma2)

Is it ok to say:??
the mean value of a new variable S is the result of mu1/mu2 ?

If you mean E{S} = E{F/A} = E{F}/E{A} = mu1/mu2

the answer is, in general no. E{S} is undefined if the probability
density of A is nonzero at A = 0.

i've seen people try to side step the difficulty by defining p(A=0) = 0

or defining probabilities in terms of Cauchy Principal Values.
However, I've never seen the attempts work when investigated in
detail.

What you need is a way to obtain the density function of
S from the density functions of F and A. I can think of one case
where p(S) is Cauchy if A and F are Gaussian. However, I don't
remember the derivation. However, the the central moments are not
defined because the density function doesn't go to zero fast
enough as abs(S) --> inf.

Hope this helps.

Greg

.

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