Hello!

I have the following problem. Let X ~N(m,s^2) and define:

Y = N(X)

Z = e^{aX+b} N(X),

where N is cumulative distribution function for standarized normal distribution (i.e. N(x)=\int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-0.5 t^2} dt)

What are the expectations of Y and Z (EY and EZ).

(I know the answer but I am looking for advice/literature how to calculate this)