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Column stochastic/2x2/Example/Special cases/Exercise

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Discuss, in the situation of example, the special cases

$p_{1} = 1$ and $p_{2} = 1$ ,
$p_{1} = 1$ and $p_{2} = 0$ ,
$p_{1} = 0$ and $p_{2} = 1$ ,
$p_{1} = 0$ and $p_{2} = 0$ ,
$p_{1} = p_{2}$ ,
$p_{1} = p_{2} = \frac{1}{2}$ .

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Mathematical exercise