HOEFFDING-TYPE PROBABILITY INEQUALITIES FOR THE DISTRIBUTION

OF SUMS OF POSSIBLY DEPENDENT RANDOM VARIABLES

In some practical problems we must compute the probability distribution of sums

of random variables which may or may not be independent. In addition, these

random variables may have different distributions. The computation of the exact

distribution is not easy and rarely of closed form. Hoeffding's Inequality and other

such inequalities may be applied, but often assume independent random variables.

Simple properties of convex functions and various other inequalities, including

Markov's Inequality and Jensen's Inequality, will be used to derive new bounds

of Hoeffding-type to compute bounds on the exact probability distribution. Although

these bounds are implicit only and not of closed form, they are much easier to

compute than the exact probability distribution. Both analytical and numerical

comparisons of these bounds are of interest.

Adviser: Prof. Steven From