Consider a Markov chain with the states $\{1,2,3,4,5\}$ and the TPM below. Please list the classes and state whether they are recurrent, transient, or absorbing$.$ Calculate the period for each class and state whether the Markov chain is irreducible or not. P$=$

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$0\mathrm{.}4$

$0$

$0$

$0\mathrm{.}3$

$0\mathrm{.}1$

$$

$0\mathrm{.}1$

$0$

$1$

$0\mathrm{.}5$

$0$

$$

$0$

$1$

$0$

$0$

$0\mathrm{.}2$

$$

$0$

$0$

$0$

$0$

$0\mathrm{.}3$

$$

$0\mathrm{.}5$

$0$

$0$

$0\mathrm{.}2$

$0\mathrm{.}4$

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