A simple branching process in discrete time. A schematic representation of a branching process. The numbers in the circles denote the generation of the cell or the number of divisions it has undergone since being labeled with CFSE. We begin with a population of undivided cells at time 0. In each timestep, each cell divides with probability γ, survives without dividing with probability δ and dies with probability α = 1 - γ - δ. At a later timestep t, sorting cells according to their CFSE content allows the numbers of cells in each generation to be estimated. The formalism we describe in this paper allows us to calculate the moments of the probability distribution of these counts at one timestep given knowledge of the number of cells in each generation at an earlier time.