For the given probability density function, find $\operatorname { Var } ( X )$ $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } \text { on } [ 0,2 ]$
A)2.000
B)1.150
C)1.500
D)0.150
E)0.800

Question

Quizplus · Accepted Answer

To find the variance, first calculate the expected value $E(X)$ and $E(X^2)$. Then use $\operatorname{Var}(X) = E(X^2) - [E(X)]^2$. After integrating, $E(X) = 1.5$ and $E(X^2) = 2.25$. Thus, $\operatorname{Var}(X) = 2.25 - 1.5^2 = 0.15$.

For the Given Probability Density Function, Find Var⁡(X)\operatorname { Var } ( X )Var(X)

For the Given Probability Density Function, Find $\operatorname { Var } ( X )$