A random variable X has the following probability distribution:
|
X |
0 |
1 |
2 |
3 |
|
P(X) |
0.1 |
0.2 |
0.3 |
0.4 |
The variance of the X will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Given distribution
$X:0,1,2,3$
$P(X):0.1,0.2,0.3,0.4$
Mean
$E(X)=0(0.1)+1(0.2)+2(0.3)+3(0.4)$
$=0+0.2+0.6+1.2=2$
$E(X^2)=0^2(0.1)+1^2(0.2)+2^2(0.3)+3^2(0.4)$
$=0+0.2+1.2+3.6=5$
Variance
$V(X)=E(X^2)-[E(X)]^2$
$=5-4=1$
The variance of $X$ is $1$.