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(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the

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$|\lambda| \sigma$

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(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the original variance is $\sigma^2$,the variance of the new observations (where each observation is multiplied by $\lambda$) is $\operatorname{Var}(\lambda X) = \lambda^2 \cdot \operatorname{Var}(X) = \lambda^2 \sigma^2$.The standard deviation is the square root of the variance.Therefore,the new standard deviation is $\sqrt{\lambda^2 \sigma^2} = |\lambda| \sigma$.

$x_i$	$92$	$93$	$97$	$98$	$102$	$104$	$109$
$f_i$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

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