Two-Type Poisson Experiment

Timeline
Distribution graph
Distribution graph

Description

The experiment is to run a Poisson process until time \(t\). Each arrival is type 1 with probability \(p\) or type 0 with probability \(1 - p\). This is known as splitting the Poisson process. In the timeline, the type 1 arrivals are shown as red dots and the type 0 arrivals as green dots. The number of type 1 arrivals \(N_1\) and the number of type 0 arrivals \(N_0\) are the random variables of interest. The values of \(N_0\) and \(N_1\) are recorded on each update in the data table. The probability density functions and moments of \(N_0\) and \(N_1\) are shown in blue in the distribution graphs and are recorded in the distribution tables.On each update, the empirical density functions and moments of \(N_0\) and \(N_1\) are shown in red in the distribution graphs and are recorded in the distribution tables. The parameters are the rate of the process \(r\), the time \(t\), and the probability \(p\). These can be varied with the input controls.