Instructions:

Suppose people arrive to an area in accordance to a homogeneous Poisson process, having

rate . Whenever a person arrives to the area, he/she stays in that area for an exponentially distributed amount of time having rate , independently of everything else.

Let Q(t) denote the number of people currently in the area at time t, and let D(t) denote the number of people that have departed from the area by time t.

1. Create R code that can be used to simulate Q(t). Recommended you use an R function, where the input is t, , and .

2. Use Monte Carlo simulation to estimate P(Q(t) = 0), for the case where t= 1, = 2, = 1.