Verified answer

if the joint probability density of x and y is given by

f(x,y)=1/4(2x+y) for 0<x<1, o<y<2, 0 elsewhere

find (a) the marginal density of x f(x)= [0,2]∫f(y)dy=[0,2]∫1/4(2x+y) dy=[0,2]{1/4(2xy+y^2/2)}=1/4(4x+2-0)=x+1/2 ,0<x<1

(b)the conditional density of y given x=1/4f(y/x)=f(x,y)/f(x)=[ 1/4(2x+y)]/[ x+1/2]= ( x+y/2)/(2 x+1)f(y/x=1/4)=y/3+1/6 ,0<y<2

2011-07-19 18:34:16 補充：

更正：[0,2]為[y：0 to 2]

2011-07-19 18:42:28 補充：

更正（a）：

f(x)= [y：0 to 2]∫f(x,y)dy=[y：0 to 2]∫1/4(2x+y) dy=[y：0 to 2]{1/4(2xy+y^2/2)}