Suppose X and Y have joint density
fX,Y(x,y) = e-x-y,
for 0 < x and 0 < y,
and fX,Y (x,y) = 0 otherwise.
a. Are X and Y independent?
b. Find P(X < 2, Y < 2).
c. Compare with the situation in which X and Y have joint density
fX,Y (x,y) = 2e-x-y,
for 0 < z < and fX,Y (x,y) = 0 otherwise. Find P(X < 2, Y < 2) in this case. Are X and y independent in this new case? Why or why not? Can you see whether X and y are independent by only looking at the joint density of X and Y?