# Robbins–Monro algorithm

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 $$M(x) = \int _{ -\infty }^{ \infty }{ yd(H|y) }$$ ?

• That’s not the expression for $M(x)$ that is mentioned in the paper. – WimC Aug 4 '19 at 6:35
• @WimC Given that the person asking is not an expert, this could clearly be a typo on his part. You could still try to answer though – Euler_Salter Nov 5 '19 at 10:19