# Math Help - independence

1. ## independence

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

2. Maybe you don't need integration. Can $p(x,y)$ be factored?

3. p(x,y) can be factorised at (1/5)(x + y/4).
but how does factorising help?

4. Can you factor out an $x$ or $y?$ If yes then they are independent, if no then they are not.

You can also figure out if they are independent, by finding the marginal densities, and seeing if multiplying the marginal densities gives you the joint density. Choose whichever works for you, but I personally follow a certain law of physics $action.$