Combinatorics of geometrically distributed random variables

Abstract

The aim of this thesis is to study various combinatorial problems relating to geometrically distributed random variables. In particular, we study sequences of geometric random variables with respect to the left-to-right maxima of the elements of the sequence. Traditionally, left-to-right maxima or records have been studied for permutations rather than sequences. For each of the parameters explained, we compute the mean and the variance both explicitly and asymptotically.