  This paper deals with the study, from a probabilistic point of view, of
logistic-type differential equations with uncertainties. We assume that the
initial condition is a random variable and the diffusion coefficient is a
stochastic process. The main objective is to obtain the first probability
density function, $f_1(p,t)$, of the solution stochastic process,
$P(t,\omega)$. To achieve this goal, first the diffusion coefficient is
represented via a truncation of order $N$ of the Karhunen-Lo\`{e}ve expansion,
and second, the Random Variable Transformation technique is applied. In this
manner, approximations, say $f_1^N(p,t)$, of $f_1(p,t)$ are constructed.
Afterwards, we rigorously prove that $f_1^N(p,t) \longrightarrow f_1(p,t)$ as
$N\to \infty$ under mild conditions assumed on input data (initial condition
and diffusion coefficient). Finally, three illustrative examples are shown.
