WBJEE · Maths · Statistics
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
- D 10.4
Answer & Solution
Correct Answer
(D) 10.4
Step-by-step Solution
Detailed explanation
Given that, \[ \begin{aligned} \sigma(X) &=2.6=\sqrt{\operatorname{var}(x)} \\ \sigma(1-4 x) &=\sqrt{\operatorname{var}(1-4 x)} \\ &=\sqrt{16 \operatorname{var}(x)} \\ &=4 \times \sqrt{\operatorname{var}(x)}=4 \times 2.6=10.4 \end{aligned} \]
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