Question

QUESTION 3 Lct 4c 2y 0 1, 0y < 1 4с + 1 rx(yz) elsewhere 0 and 4α +1 0 1 3 fx (x)= 0 elsewhere 31 Fd the margınal densıty function of Y (7) (3) 3 2 Are the random varables X and Y ındependent of each other? Justıfy your answer' 33 Calculate P(Y < X) (6) [16]

Answer 1

Given, flyla) = Yatzy , Ocach and ocycl 4 +1 31 and f(x) = 4x+1 ocaca (6 The conditional density of y given a is, flyla) = f(8.92 f(x) 42 +24 flxey) = f(a). flyla) - You T x 4x+24 f(x,y) = 2 (22+ y) - - att f.(3,4 Marginal density of y is a watu dx = 2 (122ty) *} {* 92]** 3 [i+y] (2) x any y are independent if, f(x,y) = fen) x fly) L.His a fex,y) = 2 (2x+y) Rolos e fea> xfly) = (4x+1) * ? (149 = 2 (4*+101+y since, f(x,y) & f(a)xfly) . X and Y are not independent

일 3) PCycx) =5 l ferry dyda 10 이에 (2) [] - [구+ ] . 중 |