Which of the following mentioned standard probability density functions is…

To determine the applicable distribution for discrete random variables, we distinguish between continuous and discrete probability models. Continuous distributions like Gaussian (Normal), Rayleigh, and Exponential describe variables that can take any value within a range. In contrast, the Poisson Distribution specifically models the probability of discrete events occurring over a fixed interval. Therefore, among standard distributions, Poisson is the correct choice for discrete random variables.