Consider the set Exy xy1 Suppose that we choose a point XY u

Consider the set

E={(x,y) ||x|+|y|1}.

Suppose that we choose a point (X,Y) uniformly at random in E. That is, the joint PDF of X and Y is given by

fXY(x,y)= c       (x,y)E

               0        otherwise

a.) Find the constant c.

b.) Find the marginal PDFs fX(x) and fY(y).

c.) Find the conditional PDF of X given Y=y, where 1y1.

d.) Are X and Y independent?

Thank you!

Solution