given that X and Y are joint density functions and p(x,y) =x/5+cy for 0<x<1 and 1<y<5.

are X and Y independent?

my working:

i tried to find the constant c by intergrating x from 0 to 1 and y from 1 to 5 for which the sum of the double integral is 1...i got that c=1/20

then to show that X and Y are independent, i think i need to show that P(x,y)= P(x)P(y) but for what integrals do i integrate this?

thanks