If \sigma^2 is the variance of x_1,x_2, .... x_n then 9\sigma^2 is the variance of

Correct Answer is : 4 - 3x1 , 4 - 3x2, ....... ,4 - 3xn

4 - 3x_1 , 4 - 3x_2, ....... ,4 - 3x_n

4 + 9x_1 , 4 + 9x_2, ....... ,4 + 9x_n

4 - 9x_1 , 4 - 9x_2, ....... ,4 - 9x_n

4 + 81x_1 , 4 + 81x_2, ....... ,4 + 81x_n

TS ICET 2015 Question Paper with Solutions for online practice

Question : 146 of 200

Marks: +1, -0

σ^2

is the variance of

x_1,x_2, .... x_n

then 9

σ^2

is the variance of

Solution:

Given :

σ^2

: variance of

x_1,x_2,x_3,...,x_n

∴ S.D. of

x_1,x_2,x_3,...,x_n=σ

⇒ S.D. of

3x_1,3x_2,3x_3,...,3x_n=3σ

⇒ Variance of

3x_1,3x_2,3x_3,...,3x_n=(3σ)^2=9σ^2

∴Variance of

(4–3x_1),(4–3x_2),(4–3x_3),...,(4–3x_n)=9σ^2

[Q4 is a constant term and has no effect on variance]

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