Recent content by MikeGT

I don't see how they did it when x runs from -INF to +INF. You say the exponent is not -(ax+b)^2 but it is: -[x^2+(ax+b)^2]. Apparently you're taking the extra x^2 term from the dt - integral. But how the combination can produce Φ when they integrate from -inf to +inf? They should get some...

I forgot to mention something potentially interesting. The integral S φ(ax+b) Φ(x) dx, from -INFINITY to INFINITY has been obtained by Gupta and Pillai in a technical report of the 60's as equal to Φ( b/sqrt(1+a^2) ). They mention this in a lemma but I cannot see how it was...

Suppose φ(x) and Φ(x) denote the familiar standard normal pdf and cdf. I am interested in an expression for the integral: S φ(ax+b) Φ(x) dx, from ZERO to INFINITY. Many thanks