Ian Chen 發問時間: 科學數學 · 9 年前

我有一個大學的機率數學題 ><!急

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

(b)the conditional density of y given x=1/4

please steps by steps !

1 個解答

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  • bigeye
    Lv 5
    9 年前
    最佳解答

    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)}

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