Question

Please explain how the rest of the results are achieved? (i.e. 1, x^3, ... etc)

Find the joint cdf, Fxy(x, y), for the two random variables X and Question 6 (10 points) Y with the joint pdf fxx(x, y) = {f*(1 + y) (x,y) = [0, 17, otherwise. Solution. If (x,y) = [0, 1]2, then Fax(4.) – [*a* [ay 3x2 + x) = x{2s+). Hence, (**?(2y + y2) (x,y) e [0,1], (x, y) € [1,00), Fxy(x,y) = (x,y) € [0, 1) [1,00), =(2y + y2) (x,y) € [1,00) * [0,1), x<0 or y<0.

Answer 1

9. P(x=x, Yey) - Fxx (0,4)= 122(24+43) ,46 [0, 1] x [0,1 so, it will be valid only if 3,46 Toige lip Fier (2,4)= (24+43); (2,494 [0,132 w if x>1, yol then ,P(X 25,757)P(x21,41)+ --- 2 P(XS1Y31)+ P(X>1,441) + Plxall>) + P(x>1,Y>1) =140+0+024 ☺s if Xe [0,1], ye [1,00) P(X 22, Y<9): P(X32,431) +Pexs%, 9 ) = $ (2+1) +0=322 (by mistake ge has been typed) (eu) if XE [1 po), ye [0,] P(x27,<y): P(xs), Y <9) + PIXX<, Y+y) (13) (25+42 +0 = $129+43) ☺ if aco, yco clearly P(xca, l<y)=0