Question

If the variance of a random variable $X$ is $9,$ the $S.D.$ of the random variables $-2X+5,3X-6$ and $-4X-3$ is $a,b$ and $c$ respectively. Then which of the following statement(s) is/are correct $?$

• A. $a-b=3$
• B. $b-c=3$
• C. $c-a=6$
• D. $a+b-c=3$

Answer 1

Answer: (C), (D)

$a+b-c=3$

We know, $V(lX\pm m)=l^{2}V\left(X\right);V\left(X\right)=$ variance of random variable at $X=x$
$\Rightarrow a=\sqrt{(-2{)}^2\cdot 9}=6,b=\sqrt{9\cdot 9}=9c=\sqrt{16\cdot 9}=12$