The ability of plants to grow is dependent on the presence of sufficient water to meet their transpirative needs. In a dryland vegetated ecosystem, it is typically assumed that the dominant control on growth is water availability via precipitation; moreover, the precipitation is characterized not only by its total or average amount, but by its strongly intermittent and random nature. In this talk I will discuss the dynamics of soil moisture and vegetation biomass which arise in such a system, focusing on the analytical results for the probability distributions which are available for a minimalistic point model which we have developed. Particular emphasis will be given to the non-dimensional parameters which qualitatively influence the shape of the distributions, the joint distribution structure, and the implications for stability, feedbacks, and competition.