Question

If $X$ is a variate taking values $x_1,x_2,.....x_n$ and $Y$ is another variate taking values $y_1,y_2,.....y_n$ such that $y_i=2x_i+3$ and ${\sigma }_Y=8$, then the variance of variable $Z$, taking values $\frac{3}{2}{x}_i;i=1,2,....n$ is

• A. $24$
• B. $36$
• C. $6$
• D. $18$

Answer 1

Answer: (B)

$36$

If X is a variate taking values $x_1,x_2,.....x_n$ and Y is another variate taking values $y_1,y_2,.....y_n$ such that $y_i=2x_i+3$
Given, ${\sigma }_y$ = 8 and ${\sigma }_z={\sigma }_{\frac{3}{2x}}$
According to variance property
${\sigma }_{ax+b}^2=a^2{\sigma }_x^2$
${\sigma }_y^2={\sigma }_{2x+3}^2=2^2{\sigma }_x^2$
$8^2=4{\sigma }_x^2$
${\sigma }_x^2=\frac{64}{4}=16$
${\sigma }_z^2={\sigma }_{\frac{3}{2x}}^2={\frac{3}{2}}^2{\sigma }_x^2$
${\sigma }_z^2=\frac{9}{4}\times 16=36$