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Discrete Mathematics Level pending

Let $$Y$$ be a discrete random variable such that

$P(Y= y) = \begin{cases} A, \quad y=1 \\ B, \quad y = 2 \\ 0 , \quad \text{otherwise} \end{cases}$

Find the value of $$A\times B$$ when the standard deviation of the random variable $$Y$$ is maximized.

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