Q75 / 160 · TS EAMCET 2020 (10 Sep Shift 2) · Mathematics

Assertion (A)Variance of $4 x_1, 4 x_2, \ldots, 4 x_n$ is 16 times the variance of $x_1, x_2, x_3, \ldots, x_n$Reason (R) If $y=a x+b$, then variance of $y$ is a (variance of $x)+b$ The correct option among the following is

  • A
    (A) is true, (R) is true and (R) is the correct explanation for (A).
  • B
    (A) is true, (R) is true but $(R)$ is not the correct explanation for (A).
  • Correct answer
    C
    (A) is true but $(R)$ is false.
  • D
    (A) is false but (R) is true.

Solution

Let variance of $x_1, x_2, x_3, \ldots, x_n$ be $\sigma^2$, then variance of $4 x_1, 4 x_2, \ldots, 4 x_n$ is $4^2 \sigma^2$ is $16 \sigma^2$ And variance dependent on change of scale.

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

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