Publications and Preprints

A binary operation $*$ over real numbers is said to be associative if $(x*y)*z = x*(y*z)$ and it is said to be reducible if $x*y=x*z$ or $y*w=z*w$ if and only if $z=y$. The operation $*$ is said have an identity element $\tilde{e}$ if $x*\tilde{e} = x$ for all x. We characterize different probability distributions under binary operations on the random variables.