please solve it correctly

2. [-/7 Points] DETAILS WACKERLYSTAT7 5.E.027. 0/15 Submissions Used MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER We determined that f( 1 . 7) = 6(1 - y2). Osy, sy2 = 1, 10 elsewhere, is a valid joint probability density function. ) Find the marginal density function for Y1. ,( 1 ) = . where sy 1 S Find the marginal density function for Y2. 1 2()2) = . where |sy2s (b) FindP ( Y25 - |Y, 5- ). (Enter your probability as a fraction.) (c) Find the conditional density function of Y, given Y2 = y2 f ( y , Ly 2 ) = . where Sy1 Sy 2S (d) Find the conditional density function of Y2 given Y, = y1- fly 2 ly , ) = . where sy, Sy2S (e) Find P Y2z |Y1 = - . (Enter your probability as a fraction.) Need Help? Read It 3. [-/7 Points] DETAILS WACKERLYSTAT7 5.E.031. 0/15 Submissions Used MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The joint density function of Y, and Y2 is given by f( V 1 . y2 ) = 30y 1/2". y1 - 1 sy21 - y,. 0sy, $1, o, elsewhere. (a) Show that the marginal density of Y, is a beta density with or = 2 and B = 4. How would you derive the marginal density of Y,? [ (304 7 2 2 ) By 2 Give the marginal density of Y, f , ( 1 7 ) = , where sy 1 S (b) Derive the marginal density of Y2 -1sys0, f 2 ( 1 2 ) = Osys 1 (c) Derive the conditional density of Y2 given Y, = y1. f( ) 2 1 y 7 ) = where y 1 + sy 25 - y 1 + (d) Find P(Y2 > 0 | Y, = 0.61)