This exercise is related to some of the details of the rejection sampling chain of Example 15.8 as a special case of the M-H algorithm.

(i) Show that the rejection sampling scheme described above (15.13) is equivalent to that described in Section 15.1 that involves sampling of a u from Uniform[0, 1].

(ii) Show that the jumping distribution q(x, y) satisfies (15.13).

(ii) Show that the acceptance probability of (15.12) reduces to (15.14).