Q70 / 155 · WBJEE 2019 · Mathematics

If $X$ is a random variable such that $\sigma(X)=2.6$ then $\sigma(1-4 x)$ is equal to

  • A
    7.8
  • B
    $-10.4$
  • C
    13
  • Correct answer
    D
    10.4

Solution

Given that, $$ \begin{aligned} \sigma(X) &=2.6=\sqrt{\operatorname{var}(x)} \\ \sigma(1-4 x) &=\sqrt{\operatorname{var}(1-4 x)} \\ &=\sqrt{16 \operatorname{var}(x)} \\ &=4 \times \sqrt{\operatorname{var}(x)}=4 \times 2.6=10.4 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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