Abby and Bianca Have Agreed to Meet for Lunch Between$f _ { x } ( x ) = \left\{ \begin{array} { l l }
3 x ^ { 2 } & 0 \leq x \leq 1 \
0 & \text { otherwise }
\end{array} \right.$

Question

Abby and Bianca Have Agreed to Meet for Lunch Between$f _ { x } ( x ) = \left\{ \begin{array} { l l } 
3 x ^ { 2 } & 0 \leq x \leq 1 \
0 & \text { otherwise }
\end{array} \right.$

Examlex · Accepted Answer

The Answer is

E [ h ( X , Y ) ] = \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 1 } | x - y | \cdot 6 x ^ { 2 } y d x d y = 2 \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { x } ( x - y ) \cdot 6 x ^ { 2 } y d y d x

=

12 \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { x } \left( x ^ { 3 } y - x ^ { 2 } y ^ { 2 } \right) d y d x = 12 \int _ { 0 } ^ { 1 } \frac { x ^ { 5 } } { 6 } d x = \frac { 1 } { 3 }

Abby and Bianca Have Agreed to Meet for Lunch Between $f _ { x } ( x ) = \left\{ \begin{array} { l l } 3 x ^ { 2 } & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array} \right.$

Definitions:

Abby and Bianca Have Agreed to Meet for Lunch Between fx(x)={3x20≤x≤10 otherwise f _ { x } ( x ) = \left\{ \begin{array} { l l } 3 x ^ { 2 } & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array} \right.fx​(x)={3x20​0≤x≤1 otherwise ​

Definitions:

Abby and Bianca Have Agreed to Meet for Lunch Between $f _ { x } ( x ) = \left\{ \begin{array} { l l } 3 x ^ { 2 } & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array} \right.$