(a) It is known that 0 = E[ƒ(X)], where X ~ Exp(1). What is f(.)?
(b) Write the pseudo-codes of an algorithm that generates variates from Exp(1) con-
ditional on being valued in the interval [2, ∞).
(c) Write the pseudo-codes of an algorithm that estimates with antithetic variate,
where there are 1000 variates in total.
(d) Write the pseudo-codes of an algorithm that estimates with stratified sam-
pling, where 5 strata are considered and 200 data are sampled from each stratum.
(e) Write the pseudo-codes of an algorithm that estimates with control variate,
where we use the variates in part (b) as control variates (again, 1000 variates).
Fig: 1