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)=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) $