Let W=X1+X2 and Z=X3+...+Xn
so, the question is the same as W/(W+Z)being normal,which I doubt.
and
Let X1, X2, ...., Xn be n random variable each having Gaussian Distribution with mean u and standard deviation s.
Can I say that the distribution of {(X1+X2)/(X1+X2+...+Xn)} is Gaussian? If yes what is the value of its mean and standard deviation?
Just to add to this fine reply - Read these:
Ratio distribution - Wikipedia, the free encyclopedia
http://math.tntech.edu/ISR/Introduct...newnode16.html