What Value of p Maximizes the Variance of X?

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Let the random variable X have the distribution

P(X=0) = P(=2) = p

P(X=1) = 1-2p, 0 \le p \le \frac{1}{2}

For what p is Var X maximum
 
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Write down the expression for the variance - it will be a function of p. Maximize that function.
 

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