Derivative of expectation with respect to another expectation

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Say I have binary random variables $X_1, X_2, \ldots, X_n$, and $Y$. Varaible $X_i$ and $Y$ are somehow related, and the relationship is unknown. Now, I am interested in the derivative $\frac{dE(Y)}{dE(X_i)}$. Can this quantity be obtained through the knowledge of $P(Y\mid X_i)$? If not, what is other extra information I need to determine the derivative?