# Hw4 - IE 336 Sep 26 2008 Handout#5 Due Oct 3 2008 Homework Set#4 1 Let p P = 0 q 4 q 2 q 2 r 2 r q 3r 2 4 2p be the one-step transition matrix of a

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IE 336 Handout #5 Sep. 26, 2008 Due Oct. 3, 2008 Homework Set #4 1. Let P = p q 2 r 0 q 2 3 r 2 + q 4 q 4 r 2 2 p be the one-step transition matrix of a Markov chain ( p , q , and r are parameters). (a) Determine the transition diagram of this Markov chain. (b) If p < q , is it possible that p = 17 36 ? Explain. (c) If q = 2 3 determine the values of p and r . (d) Using the values of p , q , and r computed in part (c) ﬁnd the two-step and three-step transition matrices of this Markov chain. 2. Consider the “eye color” example from class (section 2 . 21 in the book). In class we computed the ﬁrst row of the transition matrix. We also said that the entire transition matrix has the following form P = p 1 - p 0 p 2 1 2 1 - p 2 0 p 1 - p . (a) Show that the second row of the transition matrix P is indeed as shown above. (b) In class we assumed that the distribution of father’s pairs of chromosomes is Binomial with parameter p . Now, assuming that father is equally likely to have any of

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## This note was uploaded on 03/29/2010 for the course IE 383 taught by Professor Leyla,o during the Spring '08 term at Purdue University-West Lafayette.

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Hw4 - IE 336 Sep 26 2008 Handout#5 Due Oct 3 2008 Homework Set#4 1 Let p P = 0 q 4 q 2 q 2 r 2 r q 3r 2 4 2p be the one-step transition matrix of a

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