Pressing times

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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