The answer is a ½ or 0.5
To see, let us multiply these two gaussians over here--
which the exponent becomes an addition--
we can now rewrite this as follows--
when we bring the factor 2, for these two terms in to the numerator
as our 2 sigma square,
and from that we see that the new variance is 0.5
as large as the old one when applied to the squares.
So, as a result, you would have this equation over here.