Re: Probability of elements from Gaussian/normal PDF overlapping?

If we write Ra = N(Ma, Sa^2), Rb = N(Mb, Sb^2), is it useful to know
that Ra - Rb is distributed like N(Ma - Mb, Sa^2 + Sb^2)? If we want
to test that Ea >= Eb, then we are considering Ea - Eb >= 0. The z-
score of 0 is:

z = (0 - mean)/std = (Mb - Ma)/sqrt(Sa^2 + Sb^2).

and the probability is 1 - Phi(z) where Phi(z) is the cumulative
probability distribution.

.