Question: Effect of scaling and offset on average and standard deviation. Suppose \(x\) is an \(n\) -vector and \(\alpha\) and \(\beta\) are scalars.

1. Show that \(\operatorname{avg}(\alpha x+\beta \mathbf{1})=\alpha \operatorname{avg}(x)+\beta\).
2. Show that \(\operatorname{std}(\alpha x+\beta 1)=|\alpha| \operatorname{std}(x)\).

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