## The Annals of Mathematical Statistics

### The Extrema of the Expected Value of a Function of Independent Random Variables

Wassily Hoeffding

#### Abstract

The problem is considered of determining the least upper (or greatest lower) bound for the expected value $EK(X_1, \cdots, X_n)$ of a given function $K$ of $n$ random variables $X_1, \cdots, X_n$ under the assumption that $X_1, \cdots, X_n$ are independent and each $X_j$ has given range and satisfies $k$ conditions of the form $Eg^{(j)}_i (X_j) = c_{ij}$ for $i = 1, \cdots, k$. It is shown that under general conditions we need consider only discrete random variables $X_j$ which take on at most $k + 1$ values.

#### Article information

Source
Ann. Math. Statist., Volume 26, Number 2 (1955), 268-275.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177728543

Digital Object Identifier
doi:10.1214/aoms/1177728543

Mathematical Reviews number (MathSciNet)
MR70087

Zentralblatt MATH identifier
0064.38105

JSTOR