Simple conditional continuous distribution Q

Hi all,

Been going through a question I have the answer to but no working from an exercise book... can't see the logic. Wonder if anyone can lend an eye?

Q:Let be a random point chosen uniformly on the region

a) Sketch R

b) Find the marginal densities of X & Y

c) Find the conditional density of Y given X

My answers:

a) simply a kite shape with vertices at (-1,-1),(-1,1),(1,1) & (1,-1)

b) Evaluate joint density function:

By observation, the area is a tilted square with sides 1 x1 => area = 1 =>

over , now this makes sense to me, as we integrate of the 0 and (1-mod(y)) as limits given by initial conditions. By symetary, marginal of Y is the same except Y instead of X in the expression.

c)

conditional density

surely this gives the reciprocol of the marginals already found ie:

The answer in the back of the book is:

over

Now I can understand the range of y, but cant seem to see where the conditional comes from..... would make my day if someone says its a typo lol

Thanks for reading.