Hello
I am not sure what the Alpha Query would be.
However, if you have access to Mathematica, I believe that this is how would do it--and how to think about it (assuming I understand your question correctly:
Derivative of the cumulative distribution (ignoring the the fundamental theorem of calculus for a minute)
pdf = D[Integrate[
PDF[NormalDistribution[m, sd], x] +
PDF[ExponentialDistribution[decay], x], {x, -Infinity, y},
Assumptions -> Element[y, Reals] && sd > 0 && decay > 0], y]
Which gives you an expected (remembering the fundamental theorem), but not very exciting unormalized result:
pdf = Simplify[pdf]
Remembering to normalize
norm = Integrate[pdf, {y, -Infinity, Infinity},
Assumptions -> sd > 0 && decay > 0]
We recognize an additional fact about the above by looking at ever-helpful mathworld: http://mathworld.wolfram.com/Erfc.html
pdf = Simplify[ pdf/norm]