Response to the following:
1. Compare the execution times of the two proposed implementations of the Accept-Reject algorithm, as well as alternatives simulating Nsim*Nprop proposals at once when Nprop varies.
2. Show formally that, for the ratio f /g to be bounded when f is a Be(α, β) density and g is a Be(a, b) density, we must have both a ≤ α and b ≤ β. Deduce that the best choice for a and b among the integer values is a = [α] and b = [β] .