Question

Find the PDF of W = X + Y when X and Y have the joint PDF fx,y(x,y)=ĺ0 x,y(x,y) = otherwise otherwise

Answer 1

# Exy Co, y) = Sto OS X Lys & otherwise Fwcwl be the Let x+y=w., & cod f. of w then ty-w P (WEW) For (W) = - - P(X+YEW) P(x < -Y) و لاوین when oswet a - Is é dy dhe - book to (9) 1997 (w-r-xdx Ed SC20) =[wx-x)% = (032_402) Fw (W) = we ha or when oswet. Now when a {w Lo. Focus = P (WCW) = o I-P (W7, W)

4 y = 1-s t de dy w-y 4 11 -wtys dy O M = 1- to (ay-w, dy =t- [ % (yz wy)] =1((16-46) - 5 ( .492)] = - ( 16-46 +12) = 1- to (64-16 Wt way = 32-64 +16W-W2 32 -394 16w-w2 when 4CWEB = 32 of w is Herce codt Fu(w) = os wet 44 WEB 16w-w²32 32 ws 8

Now. p.dif of w is fw (W) = a FW (W) ocwe4 310 16-20 32 4swed wy P ocwc4 f (W) = 4<wka otherwise