I don't have much knowledge about advanced math. I read an article about Robbins–Monro algorithm https://pdfs.semanticscholar.org/34dd/d8865569c2c32dec9bf7ffc817ff42faaa01.pdf. And there is a formula that I really don't understand at (3) of an article. It says that Pr[Y(x) <= y] = H(y | x), such that $M(x) = \int _{ -\infty }^{ \infty }{ yd(H|y) } $.
I also read https://en.wikipedia.org/wiki/Probability_density_function. And i know $Pr(a \le X \le b) = \int _{ a }^{ b }{ f(x)d(x) }$, it seems a bit related.
So I have a few questions:
1/ what is H(x|y)?
2/ Why $M(x) = \int _{ -\infty }^{ \infty }{ yd(H|y) } $ ?