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)

$(30,\,200)$

Answer 2

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