(a) Suppose it is desired to generate Y ~ beta(o, b), where a and b are not integers. Show that using V ~ beta([a], |b]) will result in a finite value of M = suPy, fy (y)j fv (y).
(b) Suppose it is desired to generate Y ~ gamma(a, b), where a and b are not integers. Show that using V ~ gamma( [a], b) will result in a finite value of M = supy fy(y)/fv(y).
(c) Show that, in each of parts (a) and (b), if V had parameter [a] +1, then M would be infinite.
(d) In each of parts (a) and (b) find optimal values for the parameters of V in the sense of minimizing E(N) (see (5.6.12)).
(Recall that [o] = greatest integer ≤ a.)