dz wrote:
>
> Hi, anybody knows how to caculate the variance of x/y? where x and y are two
> independent variables with normal dis n(a1,b1) and
> n(a2,b2) respectively.
>
> Thank you.
This was posted by me only about two weeks ago.
|>
|> Hi Everyone.
|>
|> I've calculated the mean and variance of one variable (m1,v1) and the
mean
|> and variance of a second variable (m2,v2).
|> So, my question is what is the variance of the quotient,
response/stimulus,
|> in terms of v1 and v2 (and any other variable necessary). i.e, what
is the
|> variance of m1/m2?
|
| There are no exact formulae for the qoutient of two random variables
but
| there is approximations. One comes from a Taylor series expansion of
| m1/m2 around their means (mu1, mu2). Then take variances of both
| sides and it becomes :
|
| Var(m1/m2) \approx= (mu1/mu2)^2 x [Var(m1)/(mu1)^2 + Var(m2)/(mu2)^2
+
| Cov(m1, m2)/(mu1 x mu2)] + ...
| Of course the big question is what is Cov(m1, m2). Well if m1 and m2
are
| independent, which they may well be if the original variables say, y1
| and y2 were, then Cov() = 0.
--
---
Julian Taylor
Biometrics
Adelaide University
[EMAIL PROTECTED]
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