$X$ is a random variable with known pdf. I do have the expectation of a function of X. $\mathbb{E}[f(X)] = A $. Is f unique?
I also have multiple sets of vector $(x_1, ..., x_n)_t$ known, where $t$ shows various samples, $\sum_{i=1}^{n} f(x_{i, t}) $, $\sum_{i=1}^{n} f'(x_{i, t})$, and higher-order derivatives. How can use this fact to uniquely determine f, I am thinking about mean square error to find $f$ from a class of function like a polynomial. I was wondering if there is a way to do it more rigorously in a simple manner.