For what values of [math]a[/math] and [math]b[/math] is the function [math]f(x,y)[/math] given below a valid joint density function?

[[math]] f(x,y) = \begin{cases} ax + by, \quad 0 \leq x \leq y \leq 1 \\ 0 \quad \textrm{otherwise} \end{cases} [[/math]]

• [math]2a + b = 6 [/math]
• [math]2a + b = 6 [/math] and both [math]a [/math] and [math]b[/math] must be non-negative
• [math]a + b = 2 [/math] and both [math]a [/math] and [math]b[/math] must be non-negative
• For all non-negative [math]a[/math] and [math]b[/math]
• There are no values [math]a[/math] and [math]b[/math] that give a valid joint density