Deniz,
Here is a rough draft of the solution. Hope that this helps.
Maureen
Here is a rough draft of the solution. Hope that this helps.
Maureen
Corr(ab) = cov(ab)/sqrt(var(a)*var(b))
a= (x-y)
b = x
ab = x^2 – xy
Cov(ab) = (sum(ab) – sum(a)sum(b)/n)/(n-1)=
[Sum(x^2) – sum(xy) – (sum(x-y)*sum(x))/n]/(n-1)
= [Sum(x^2) – sum(xy) – (sum(x)^2 – sum(y)*sum(x))/n]/(n-1)
= [Sum(x^2) – sum(x^2)/n]/n-1 – [sum(xy) –sum(x)*sum(y)/n]/(n-1)
= variance(x) - cov(x,y)
since x and y are independent then cov(x,y) = 0.
So
Corr = variance(x)/sqrt(Var(x-y)*var(x)) = sqrt(var(x))/sqrt(var(x)+var(y))
Since Var(x-y) = var(x) + var(y).
From: Deniz Senturk <dnz_senturk@...>
To: Statistics Group <statisticians_group@...>
Sent: Wednesday, February 4, 2009 2:08:06 PM
Subject: [Statisticians_group] RE: Correlation coefficient of X -Y
Sorry,
the question would be the correlation coefficient between X and Z
(Z = X-Y)
From: dnz_senturk@ hotmail.com
To: statisticians_ group@yahoogroup s.co.in
Subject: Correlation coefficient of X -Y
Date: Wed, 4 Feb 2009 20:24:56 +0200
Hi,
I have a question about corr.coefficients.
X is an independent variable with mean ?1 and variance σ1 2
Y is an independent variable with mean ?2 and variance σ2 2
Let Z= X - Y
How can I find the correlation coefficient of Z in terms of means and variances?
Thank you,
Regards,
Deniz.
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