The Symmetric Property states that for all real numbers x and y , if x=y , then y=x . Transitive Property. The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .

Step-by-step explanation: you couldnt have looked it up on ggle?...haha -_-'

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2 years ago

Let P = 0.50.30.50.7 be the transition matrix for a Markov chain with two states. Let x0 = 0.50.5 be the initial state vector fo

pav-90 [236]

Answer:

Probability distribution vector = $\left(\begin{array}{c}0.375\\ 0.625 \end{array} \right)$

Step-By-Step Explanation

If $P=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right)$ is the transition matrix for a Markov chain with two states.

$x_{0}=\left(\begin{array}{c}0.5\\ 0.5 \end{array} \right)$ be the initial state vector for the population.

$X_{1}=P x_{0}=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right) \left(\begin{array}{c}0.5\\ 0.5 \end{array} \right) =\left(\begin{array}{c}0.4\\ 0.6 \end{array} \right)$

$X_{2}=P^{2} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)$

$X_{3}=P^{3} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)$

$X_{30}=P^{30} x_{0}=\left(\begin{array}{c}0.37499\\ 0.625 \end{array} \right)$

In the long run, the probability distribution vector Xm approaches the probability distribution vector $\left(\begin{array}{c}0.375\\ 0.625 \end{array} \right)$ .

This is called the steady-state (or limiting,) distribution vector.

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2 years ago