given a non-increasing vector $b\in R^n$ I would like to calculate the expected argmax of the function f(b) = i*b_i. More clear and mathematical meaning. It's worth mentioning that I assume that the vector $b$ is drawn from some known distribution $F$. All my attempts so far used the expected vector $b$, but I don't want to use this expected vector, but rather use the expectation on the whole term, as is written in the image above. Answers with (mathematical properties) limitations of $F$ (such as regularity or liphshiz) are also welcomed.
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized. In contrast to global maxima, which refers to the largest outputs of a function, arg max refers to the inputs, or arguments, at which the function outputs are as large as possible.
Thx in advance!
