Bivariate N~ Distribution

[drfg2008]

(This thread refers to "Bivariate Normal Distribution - Oct.10 )
[as an example for a bivariate N~distr.: Y ~N (µ=15.73, s= 7.24) , X ~N (µ=14.17, s= 8.19), r(X,Y) = -0.047]

I have a table of 5 columns. The five columns contain statistical moments of two intercorrelated Normal distributions: µ(1), µ(2), s(1),s(2), r(1,2).

Where

µ(1) is the mean of distribution 1 (X),
µ(2) is the mean of distribution 2 (Y),
s(1) is the standard deviation of distribution 1 (X),
s(2) is the standard deviation of distribution 2 (Y),
r(1,2) is the correlation (Pearson) between distribution 1 and distribution 2 (X,Y).

Does anyone have a suggestion (or a syntax example) how to compute what proportion of the bivariate distribution is in the range (Y>X+1)



Data example:
 
case   µ1      µ2     s1     s2     r      proportion

1     15.73  14.17   7.24   8.17   -0.047    ?
2     16.12  15.56   8.14   9.32   -0.056    ?
3     17.78  11.47   6.34   7.78   -0.037    ?
4     14.98  19.32   6.24   6.56   -0.097    ?
5     12.32  21.84   4.24   6.56   -0.044    ?


Thank you.

[David Marso]

First of all in the future,
Please continue the earlier thread to maintain context rather than beginning a new thread.
No fish today, just 2 helpful prods with the clue stick.
---
Hint:  The difference of 2 normally distributed variables is also normally distributed.
The variance of a linear combination is C1**2*Var1+C2**2*Var2+ 2*C1*C2*Cov(Var1,Var2)
Where C1=1 and C2=-1 in this case.
---

drfg2008 wrote

(This thread refers to "Bivariate Normal Distribution - Oct.10 )
[as an example for a bivariate N~distr.: Y ~N (µ=15.73, s= 7.24) , X ~N (µ=14.17, s= 8.19), r(X,Y) = -0.047]

I have a table of 5 columns. The five columns contain statistical moments of two intercorrelated Normal distributions: µ(1), µ(2), s(1),s(2), r(1,2).

Where

µ(1) is the mean of distribution 1 (X),
µ(2) is the mean of distribution 2 (Y),
s(1) is the standard deviation of distribution 1 (X),
s(2) is the standard deviation of distribution 2 (Y),
r(1,2) is the correlation (Pearson) between distribution 1 and distribution 2 (X,Y).

Does anyone have a suggestion (or a syntax example) how to compute what proportion of the bivariate distribution is in the range (Y>X+1)



Data example:
 
case   µ1      µ2     s1     s2     r      proportion

1     15.73  14.17   7.24   8.17   -0.047    ?
2     16.12  15.56   8.14   9.32   -0.056    ?
3     17.78  11.47   6.34   7.78   -0.037    ?
4     14.98  19.32   6.24   6.56   -0.097    ?
5     12.32  21.84   4.24   6.56   -0.044    ?


Thank you.