On Wed, 14 Jun 2000, Kumara Sastry wrote:
> Suppose I have two random variates X,Y following normal distribution,
> X = N(u1,v1)
> Y = N(u1-u2, v1(1-z))
>
> where u1 is the mean and v1 is the variance. u2 < u1 and z ranges
> between 0-0.95. Is there an analytical expression for the covariance of
> X and Y in terms of u1,v1, u2, and z?
The short answer is "No." A less short answer is, "Not without more
information." Since the covariance is independent of the means of the
variables, any such expression would not involve u1 or u2.
If you know the correlation r between X and Y (which itself is
independent of means and variances), the covariance of X and Y is
r s_x s_y
where s_x = the standard deviation of X and s_y = the standard deviation
of Y. In terms of your variances, the covariance c would be
c = r v1 (1-z)^0.5
where you may prefer to think of (1-z)^0.5 as the (positive) square
root of (1-z).
If you do not know the correlation, nor have any other information
concerning the covariance, you do not have enough information to
determine it. There is nothing in what you have reported that would
restrict the covariance in any way: r could be any value between -1
and +1.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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