# Consider a renewal process. Let X be the interrenewal times;

19 / 01 / 2019 Maths

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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."

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