Consider a random walk {Xn : n = 0, 1, . . . } on the integer line S = {. . . , −2, −1, 0, 1, 2, . . . } and suppose that Pi,i+1 =1/3 and Pi,i-1 = 2/3 for i ∈ S. a) Draw a transition state diagram. b)True or False? All states are recurrent. Justify your answer. c) What is the long-run proportion of time spent in each state, πi? d) If Pi,i+1 = Pi,i-1 = 1/2 instead, how do parts (b) and (c) change? please answer parts a, b, c and d.

Consider a random walk {Xn : n = 0, 1, . . . } on the integer line S = {. . . , −2, −1, 0, 1, 2, . . . } and suppose that Pi,i+1 =1/3 and Pi,i-1 = 2/3 for i ∈ S. a) Draw a transition state diagram. b)True or False? All states are recurrent. Justify your answer. c) What is the long-run proportion of time spent in each state, πi? d) If Pi,i+1 = Pi,i-1 = 1/2 instead, how do parts (b) and (c) change? please answer parts a, b, c and d.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 8EA

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Question

Consider a random walk {X_n : n = 0, 1, . . . } on the integer line S = {. . . , −2, −1, 0, 1, 2, . . . } and suppose that P_i,i+1 =1/3 and P_i,i-1 = 2/3 for i ∈ S.

a) Draw a transition state diagram.

b)True or False? All states are recurrent. Justify your answer.

c) What is the long-run proportion of time spent in each state, π_i?

d) If P_i,i+1 = P_i,i-1 = 1/2 instead, how do parts (b) and (c) change?

please answer parts a, b, c and d.

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