Math Problem Statement
Let (Xn) be a process on {0, 1} with transition matrix P = ( 1/3 2/3 1/5 4/5 ) . Find the eigenvalues of P and find the stationary probability vector π. If q(0) = (1/2, 1/2) find q(1) and q(2). Using a computer, e.g. with R, find q(20) and explain this value in relation to π.
Solution
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Math Problem Analysis
Mathematical Concepts
Markov Chains
Matrix Algebra
Eigenvalues
Probability Theory
Formulas
det(P - λI) = 0
πP = π
q(n) = q(0)P^n
Theorems
Eigenvalue Theorem
Stationary Distribution Theorem
Suitable Grade Level
Grades 11-12
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