Some Statistical Properties of Total Forage Consumption by Grazing Animals on a Rangeland

Owing to a variety of factors, the total forage consumed by grazing animals on a rangeland is a random variable. Although this fact has been recognized in the extant literature, to the best of our knowledge, there are no studies that have analyzed the statistical properties of this random variable. Therefore, we begin by constructing a stochastic model of forage consumption by grazing animals on a rangeland and then we shed light on two specific questions. First, we compute the mean and the variance of the total forage consumed by the grazing animals in a random time tau. Next, we show how the probability distribution function of the total forage consumed can be calculated recursively using a particular equation and an initial value condition