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BITSAT 2017
Exam
BITSAT
Year
2017
Subject
Mathematics
Chapter
Statistics

BITSAT 2017 · Mathematics · Statistics

If the variance of the observations x _ 1 , x _ 2 , , x _ n is σ ^...

If the variance of the observations x1,x2,……,xn{x}_{1}, {x}_{2}, \ldots \ldots , {x}_{n} is σ2{σ}^{2}, then the variance of αx1,αx2,……,αxn,α≠0\alpha{x}_{1}, \alpha{x}_{2}, \ldots \ldots , \alpha{x}_{n}, \alpha \ne 0 is

Options

  1. Aσ2{σ}^{2}
  2. Bασ2\alpha{σ}^{2}
  3. Cα2σ2{\alpha}^{2}{σ}^{2}
  4. Dσ2α2\dfrac{\sigma2}{\alpha2}

Correct answer

C. α2σ2{\alpha}^{2}{σ}^{2}

Step-by-step solution

Variance =1nΣ(x−x¯)2=σ2= \dfrac{1}{n}Σ ( x - \overset{¯}{x}{)}^{2} ={σ}^{2}

New variance =1nΣ(\alphax−αx¯)2= \dfrac{1}{n}Σ ( \alphax - \alpha\overset{¯}{x}{)}^{2}

=α21nΣ(x−x¯)2=α2σ2= {\alpha}^{2}\dfrac{1}{n}Σ ( x - \overset{¯}{x}{)}^{2} = {\alpha}^{2}{σ}^{2}

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