A random sequence of convex polygons is generated by picking two edges of the current polygon at random, joining their midpoints, and picking one of the two resulting smaller polygons at random to be the next in the sequence. Let Xn +3 be the number of edges of the nth polygon thus constructed. Find E(Xn) in terms of Xo, and find the stationary distribution of the Markov chain X.

A random sequence of convex polygons is generated by picking two edges of the current polygon at random, joining their midpoints, and picking one of the two resulting smaller polygons at random to be the next in the sequence. Let Xn +3 be the number of edges of the nth polygon thus constructed. Find E(Xn) in terms of Xo, and find the stationary distribution of the Markov chain X.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 18EQ

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