Hi, I have some troubles with question 7 from the CT6 exam of September 2008. Does anybody know how to match this question with the course notes. I can't find an example of approximating an integral like this. And the solution of the examiners' report isn't clear at all. Part (i): In the course notes I found that theta^hat = (1/n)*sum[x_t, t=1..n]. In the solution it is given that: theta^hat = (1/n)*sum[exp(U_t)-1, t=1..n]. So this mean that x_t = exp(U_t)-1. But why? What is going on here? Did anybody found out what this question is about. Thanks.
Hi Barbados There is actually no mention of the use of Monte Carlo estimation to calculate integrals in the Core Reading and so we feel that this question was a little bit unfair! To estimate the integral over the range (0,1) we use our n observed values from the uniform distribution over (0,1). These are substituted in for x in the expression exp(x) -1. The integral is then approximated by averaging over n the sum of these expressions. I hope this helps a bit. Good luck! Elizabeth
