Question

For each of the exercises in this section that requires a simulation, see if you can think of a way to use control variates or antithetic variates to reduce the variance of the simulation estimator.

Short answer

Antithetic variates to reduce the variance of the simulation estimator are considered in exercises 4, 6, and 10.

Step-by-step solution

Reduce the variance of the simulation estimator

Consider exercises 4, 6, and 10. Perhaps in another exercise, one of the methods could also be used. See solutions for exercises 14 and 16.

In exercise 4, part (b), the method could be used in this case set function h(x) to be\({e^{ - x}}\).

In exercise 6, part(a) and part(b), the quotient of the two functions is monotone, implying that the antithetic variates method could be used. See the solution to exercise 6.

Exercises 6 in this section

The method could be used in exercise 6, part (a). In this case, set function h(x) to be\(x{e^{ - {x^2}/2}}\). See the solution to exercise 6.

Exercise 10 is based on exercise 6, so one could use both methods described earlier.

Here, the final result is considered for exercises 4, 6, and 10.