Math Problem Statement
- Show that (a, b) is a fixed point of the stochastic matrix P = the associated fixed probability vector? [[1 - b, b], [a, 1 - a]] What is
Hence write down the fixed probability vector of each of the following matrices. P1 = [1323] P2=2313 P3 = [ 7/10 3/10 8/10 2/10
P₁ and
(1-a) (1-b)+a², (1 b(1-b)+a(1-b), b2
shall show that a₁₂ + b₁ = 1 an
wy
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Probability Theory
Matrix Theory
Formulas
Fixed point condition: πP = π
Stochastic matrix property: sum of each row = 1
Theorems
Fixed Point Theorem for Stochastic Matrices
Suitable Grade Level
Undergraduate
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