Find the Condition on the Non-Negative Constants a and B $p ( x , y ) = \left\{ \begin{array} { c l } a x + b y , & 0 \leq x \leq 8,0 \leq y \leq 8 \\0 & \text { otherwise }\end{array} \right.$

Multiple Choice

Find the condition on the non-negative constants a and b for p(x, y) to be a joint density function, where $p ( x , y ) = \left\{ \begin{array} { c l } a x + b y , & 0 \leq x \leq 8,0 \leq y \leq 8 \\0 & \text { otherwise }\end{array} \right.$

A) $a + b = \frac { 1 } { 256 }$
B) $a + b = \frac { 1 } { 32 }$
C) $a + b < \frac { 1 } { 256 }$
D) a=b
E) $a + b = \frac { 1 } { 512 }$