If each observation of a dist., whose variance is `σ^2` , is multiplied by `lambda`, then the S.D. of the new observations is

Answer

`Rightarrow S . D(lambda x)=|lambda| cdot sigma`

Explanation

We know, `V ar (aX+b)`=`a^{2}.` `V ar (x)`



Here `b=0, a=\lambda`



$$
\begin{aligned}
&\therefore \text { Required variance }=\mathrm{V} \operatorname{ar}(\lambda \mathrm{x})=\lambda^{2} \cdot \mathrm{V} \operatorname{ar}(\mathrm{x})=\lambda^{2} \cdot \sigma^{2} \\
&\Rightarrow \mathrm{S} . \mathrm{D}(\lambda \mathrm{x})=|\lambda| \cdot \sigma
...