  The study of the dynamics of the size of a population via mathematical
modelling is a problem of interest and widely studied. Traditionally,
continuous deterministic methods based on differential equations have been used
to deal with this problem. However discrete versions of some models are also
available and sometimes more adequate. In this paper, we randomize the Pielou
logistic equation in order to include the inherent uncertainty in modelling.
Taking advantage of the method of transformation of random variables, we
provide a full probabilistic description to the randomized Pielou logistic
model via the computation of the probability density functions of the solution
stochastic process, the steady state and the time until a certain level of
population is reached. The theoretical results are illustrated by means of two
examples, the first one consists of a numerical experiment and the second one
shows an application to study the diffusion of a technology using real data.
