I had an interesting email exchange [or rather exchange of emails] with a (German) reader of Introducing Monte Carlo Methods with R in the past days, as he had difficulties with the validation of the accept-reject algorithm via the integral
in that it took me several iterations [as shown in the above] to realise the issue was with the notation
which seemed to be missing a density term or, in other words, be different from
What is surprising for me is that the integral
has a clear meaning as a Riemann integral, hence should be more intuitive….