Prove that \( \sum_{r=0}^{n} r^{2}{ }^{n} C_{r} p^{r} q^{n-r}=n p q...

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Prove that \( \sum_{r=0}^{n} r^{2}{ }^{n} C_{r} p^{r} q^{n-r}=n p q+n^{2} p^{2} \), if \( p+q=1 \).
\( \mathrm{P} \)
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