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Standard Deviation

If X, Y are...

Question

If $X, Y$ are independent then $S D (X - Y)$ is:

S D (X) - S D (Y)

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S D (X) + S D (Y)

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\sqrt{S D (X) + S D (Y)}

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None of these

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Solution

The correct option is C $S D (X) + S D (Y)$
$S D (X - Y) = S D (X) + S D (- Y)$

$⟹ S D (X - Y) = S D (X) + S D (Y)$ (since, $S D (a X) = | a | S D (X)$ )

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