Question

If the variance of a random variable X is ${\sigma }^2$, then the variance of the random variable X-$5$ is?

• A. $5{\sigma }^2$
• B. $25{\sigma }^2$
• C. ${\sigma }^2$
• D. $2{\sigma }^2$

Answer 1

Answer: (C)

${\sigma }^2$

If variance of $X=k$, then variance of $ax+b=a^{2}k$

Here $a=1$ & $b=-5$

$\therefore$ variance of $x-5={\sigma }^2$