How can I solve this question 6.20? 6.20. The joint density of X and Y is given byxe-(+)f (x, y) =Are X and Y independent? If, instead, ƒ(x, y) were given byf(x, y) =(20x → 0, у > 0otherwisewould X and Y be independent?0 < x

Hello! As you have posted 2 different questions, we are answering the first question. In case you require the unanswered question also, kindly re-post them as separate question. Given information: fx,y=xe-x+y, x>0, y>0 Consider, fx=∫y=0∞fx,ydy =∫y=0∞xe-x+ydy =xe-xe-y-10∞ =-xe-x*e-∞-e-0 =xe-x, x>0 fy=∫x=0∞fx,ydx =∫x=0∞xe-x+ydx =e-y-xe-x-e-x0∞ =e-y*e-∞-e-0 =e-y, y>0 Condition for Independence: fx,y=fx*fy if X and Y are independent. Consider, fx*fy=xe-x*e-y =xe-x+y =fx,y That is, the condition for independence is satisfied. Thus, X and Y are independent.