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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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
Transcribed Image Text: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.
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