In this exercise, I should do the following subquestions for θ=P(X+Y≥15) where X∼Exp(0.5) and Y∼Exp(0.25) both X and Y are independent.

Implement the following estimators for θ:

(i) The raw simulation estimator.

(ii) The antithetic estimator.

But the exercise here restrict the methods that I can use, so it's only allowed to use the uniform random numbers U(0,1) and the program R should be used here.

My problem is that I don't know how to get started with this exercise. I know a little bit of the theory about variance reduction, but not how to get started with (i) and (ii).

Any hints or examples would be a big help for me.