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4 years ago

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Which expression can you simplify by combining like terms? 6d2+5cd?3dc+8 12c2?8d2c+3dc+4 7d2?3c2+6d?c 16c2+8cd+7c?8d

1 answer:

Archy [21]4 years ago

4 0

Simplify combining like terms on 8d2c+3dc+47d2

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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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3 years ago