joint pdf

Can anyone help me out with this problem... Here is what i get:
a) c = 1/2
b) Marginal pdf of x = 2 - x
c) y
d)1/3
e) no because fx(x) * fy(y) != fxy(x,y)

My work:



Can anyone double check my work?

is there anything i can clear up?
Im not very good with paint... sorry.

No good. You started out with a rectangular region. Get rid of the white space below the blue region and above the x-axis.

Work with the lines

y = 1
y = 1 - x ==> x = 1 - y
y = x - 1 ==> x = y + 1

\(\displaystyle \int_{0}^{1}\int_{1-y}^{y+1} c\;dx\;dy\;=\;1\)

Or, to save on postage, you can just look at the geometry. Area = ½*Base*Height = ½*2*1 = 1

Now what?