Determining Bounds on Expected Values of Certain Functions
Determining Bounds on Expected Values of Certain Functions
Let $\mathfrak{F}$ be the collection of cumulative distribution functions on $(- \infty, \infty)$ and $\mathfrak{F}_{\lbrack a, b\rbrack}$ that subset of $\mathfrak{F}$ all of whose elements have $F(a - 0) = 0$ and $F(b) = 1$. Let $\mathfrak{F}^{(\mu_1, \mu_2, \cdots, \mu_k)} (\mathfrak{F}^{(\mu_1, \mu_2, \cdots, \mu_k)}_{\lbrack a, b\rbrack})$ be the class of …