Find the expected value of the random variable whose density function is $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } , 0 \leq x \leq 2$ .
A) $\frac { 5 } { 2 }$
B) $\frac { 5 } { 8 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 3 } { 8 }$
E) none of these

Question

Quizplus · Accepted Answer

The expected value $E(X)$ is calculated by integrating $x \cdot f(x)$ over the interval [0, 2]. The integral $\int_0^2 x \cdot \frac{3}{8} x^2 \, dx$ evaluates to $\frac{3}{2}$.

Find the Expected Value of the Random Variable Whose Density f(x)=38x2,0≤x≤2f ( x ) = \frac { 3 } { 8 } x ^ { 2 } , 0 \leq x \leq 2f(x)=83​x2,0≤x≤2

Find the Expected Value of the Random Variable Whose Density $f ( x ) = \frac { 3 } { 8 } x ^ { 2 } , 0 \leq x \leq 2$