Subject: HW 2 problem 15, p.146 Lefebvre Hello STAT 650 class --- I talked very briefly about this problem #15 in class today. The problem is not very well stated. The key point is to ask in what sense the "limit" is desired (or possible). First, since previous problems in the same text do talk about "finding limits if they exist", I take the main point of the problem to be checking (with mathematical justifications) whether the limit can exist (with positive probability) for the random sequence {p_n}. A second related problem [which I do not think the book meant to ask, but which we can do anyway] is to find the limiting probability distribution for large n of p_n among its possible values 1/2, 2/3 and 3/4. The key point there is to note that if Y_n denote the outcomes of the successive independent fair coin-tosses, then Z_n = (Y_{n-1},Y_n) is a Homogeneous-transition Markov Chain with a four-point state space, and p_n is a simple function of Z_n. I will show in class that p_n itself is NOT a Markov chain on its 3-point value space. Eric Slud