Two dice A and B are rolled, giving ,.

Question

Two dice A and B are rolled, giving $\alpha,\beta$. If the variance of $\alpha-\beta$ is $\dfrac{p}{q}$ (coprime), find the sum of the positive divisors of $p$.

Accepted Answer

Since $\alpha,\beta$ independent, $	ext{Var}(\alpha-\beta)=	ext{Var}(\alpha)+	ext{Var}(\beta) = 2	imes\dfrac{35}{12}=\dfrac{35}{6}$.

$p=35=5	imes7$; sum of divisors $=(1+5)(1+7)=48$.

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