Question

Quote 10 Let And w t erende vector with a bebe e try Find the natural c a trix of the rules for Qui 11 lalele 3 = y): SS10 SS 1/2) arides with t y wel XlYle m pection 1 0 otherwise the value of (b) the w (e) LO a y to any probability sky L the of the Cally Quo 12 The type of kan wariables the li s ty Ir I+ CICIOS b) as the mos Qomi 18 and the Tudom riable t X with the following Y it fx AY-X De baty. Note that b) Latina de variable with questional Superi od <1/2 the fact of Y. WhZ-Y+ Y haised in ete the The the y act of 2 Q 15 Awang i s in the cities, J., L. The there I n The Furto the data of the citi 14) (1 ) 1 1 -2-45 LA X hows from the this the STX Questi 16 Getaria de S ant PUXIST) state Probe 4.61 (b) (Hint: t r y, the 151 of the Questi IT This year, the brow s X pak pelay where del The e company reason This the la test there

Answer 1

X +Y 2X - Y -3) + (1 1X 2 -1) (Y Micon vector = (EKO) - (%) +(-1)(*) - (). Disp (™) = (1, -1) (15 35) (2.) = (20 33).

11. (a) x 1" ("(x +29)dy) dx = 1 or, * 1 [ry + y2]” dr = 1 or, ki 1 + 1]dx = 1 or, k=2. (6) The marginal pdf of X is 2.1 +1 fx (2) = 2 (x + 2y)dy = 1/2 0<x<1 = 0 otherwise The marginal pdf of Y is fy(y) = 2 (2 + 2y)dt = 4y + 1; 0<y <1/2 = 0 otherwise (c) The conditional pdf of Y given r: f(x,y) 42 + 2y). 2; 0<y<1/2 fx(C) 2.1 +1: = 0 otherwise 2437 (d) E(Y - 4 1/2 4 2) = 2x+1). ) = y(x+2y)dy = . 2.1 +1 cy2 2 3.1 +2 6(2.6 +1) '