# Normal Law

#### mikoko

##### New Member
Hi there
will be very greatfull if anyone can help:
If X represent the daily yield of the S&P500(US Stock indices) and Y represent the daily yield of the DAX(German Stock Indice). Let assume that X and Y are Following a Normal Law and are independent.
X~N(M1,S1) M1 mean of X and S1 its standard deviation
Y~N(M2,S2) M2 mean of Y and S2 its standard deviation
Looking to calculate the probability:
P(X>Y and X>0)

#### BGM

##### TS Contributor
In this question you need to invoke the bivariate normal joint CDF, which in turns has no closed form solution unless for special cases.

You may use, e.g. R and search for packages to calculate the joint probability numerically, if the parameters are provided.

#### rogojel

##### TS Contributor
Assumig independence would be rather questionable, unless this is an exercise,BTW.

In real life I would just simulate the two series and estimate the probability.

regards

#### mikoko

##### New Member
thx very much , I was hoping that we can have an analytic solution to this problem.
Seems like simulating historically with a large number of occurrence could give me a good estimation.