where 
is the waiting time for the ith event to occur and each 
is
generated from a Poisson process with common rate parameter 2,
Create a matrix X of dimension (100,150) such that each
of the 100
rows of X contains observations of
where is the waiting time for the ith event to occur and each is
generated from a Poisson process with common rate parameter 2,
using the scheme in Problem 4.5.6 with
t=30.
By substituting 
for 
in the expression for the
variance of this estimate, come up with a standard error for each of
your 100 estimates. Now, keeping in mind that the standard error is an
approximation to the standard deviation
of your estimate, compare the mean of your
100 standard errors with the sample standard deviation
of your 100 estimates. How
do these two numbers compare?
using the scheme in Problem 4.5.7 with
n=30 for each of the 100 simulations in X.
By substituting 
for 
in the expression for the
variance of this estimate, come up with a standard error for each of
your 100 estimates.
Again compare
the mean of your
100 standard errors with the sample standard deviation
of your 100 estimates.