Ray, Thanks for your response. (I do not have enough stats to understand it fully though) If you could suffer me once more, I have contrived an example, hopefully to benefit my understanding. Can I please ask you to walk me through to the solution? A = N(mean 0,variance 1), B = N(2,2) and C = N(3,4) What is the probability that A is greater than B and C Thanks again, Dave
[EMAIL PROTECTED] (Ray Koopman) wrote in message news:<[EMAIL PROTECTED]>... > > I assume that you mean (A,B,C) is trivariate normal, with known mean > vector and covariance matrix. Let X = A-B and Y = A-C. Then (X,Y) is > bivariate normal with known mean vector and covariance matrix, and your > question is "What is the probability of observing (X > 0, Y > 0)?". > > Let u = Mean(X)/SD(X), v = Mean(Y)/SD(Y), w = Cov(X,Y)/(SD(X)SD(Y)). > Let F(z) denote the standard normal cdf, and let f(x,y,r) denote > the bivariate standard normal pdf. Then Pearson (~1901) showed that > your desired probability is Integral_0^w f(u,v,r)dr + F(u)F(v). . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
