## Michigan Tech Publications

#### Title

An optimal upper bound on the tail probability for sums of random variables

Article

10-22-2019

#### Department

Department of Mathematical Sciences

#### Abstract

Let \$s\$ be any given real number. An explicit construction is provided of random variables (r.v.'s) \$X\$ and \$Y\$ such that \$\sup{P}(X+Y\ge s)\$ is attained, where the \$\sup\$ is taken over all r.v.'s \$X\$ and \$Y\$ with given distributions.

#### Publication Title

Theory of Probability & Its Applications

COinS