Question

Let $X$ be a random variable with its expectation $E(X)=3$ and its variance $V(X)=2$ . If $V$ is another random variable defined by $Y=10X,$ then the ordered pair $(E(Y),V(Y))$ is equal to

• A. $(10,200)$
• B. $(30,20)$
• C. $(10,20)$
• D. $(30,200)$

Answer 1

Answer: (D)

Given, $E(X)=3,V(X)=2$ We know that, if $y=aX+b,$
then $E(y)=E(aX+b)=aE(X)+b$ and $V(y)=a^{2}V(X)+b$
Here, we have $y=10X$
$\therefore$ $E(y)=E(10X)=10E(X)$
$10\times (3)=30$
and $V(y)=V(10X)$
$={(10)}^{2}V(X)$
$=100(2)=200$
Hence, $\{E(y),V(y)\}=(30,200)$