1. ## joint distribution problem

The density fnc. of X and Y is
f(x,y)=x+y for 0<x<1, 0<y<1 and 0 otherwise.

a-Are X and Y independent?
b-Find the density function of X
c- Find P(X+Y<1)

2. (a) dependent by inspection, the joint density does NOT factor.

(b) $f_X(x)=\int_0^1 f(x,y)dy=x+.5$ on (0,1).

and I'll let you do

(c) $\int_0^1\int_0^{1-x} f(x,y)dydx$.