Consider a renewal process. Let X be the interrenewal times; and let I and R be the length of an interval interrupted at random and its remainder, respectively. The following BASIC simulation calculates the average values of X, I, and R (based on 10,000 replications of I and R, where T is a random interruption point).
100 FOR j=1 TO 10000 110 S=0 120 T = -1000*LOG(1-RND) 130 X= 140 c=c+1 150 SX=SX+X 160 S=S+X 170 IF Sa. Run the simulation for the case when X is exponentially distributed (that is, the renewal process is a Poisson process) with E(X) = 1. Fill in the following table.
E(X) E(I) E(R) theory simulation theory simulation theory simulation
Comment on the assertion: "It is intuitively obvious that E(I) = E(X) and E(R) = E(X) / 2."