Re: [商管] [統計]-隨機變數求解
(1)
Pr(X = 1 , Y = 1 ) = Pr(X = 1 , Y≦1 ) = 0
3
Pr(X = 1 , Y = 2 ) = Pr(X = 1 , Y≦2 ) - Pr(X = 1 , Y≦1 ) = -----
c
5
Pr(X = 1 , Y = 3 ) = Pr(X = 1 , Y≦3 ) - Pr(X = 1 , Y≦2 ) = -----
c
2
Pr(X = 2 , Y = 1 ) = Pr(X = 2 , Y≦1 ) = -----
c
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可以求出混合機率密度表如下
X
1 2 3
2
1 0 ----- 0
c
3 3 3
Y 2 ----- ----- -----
c c c
5 5 5
3 ----- ----- -----
c c c 加總為 1, 可解出 c = 26
(2)
f(X,Y) 2 2
f(X∣Y=1) = --------- = (------) / (------) = 1 where x = 2
f(Y) 26 26
E(X∣Y=1) = 1 * 2 = 2
(3)
cov(X,Y) = EXY - EXEY = 0 X與Y無線性關係
(4)
Z = (X-2)^2 where x = 1,2,3 => z = 1,0,1 => z = 1,0
8 8 8
f(z) = ------ + ------ = ------ where z = 1
26 26 13
10 5
f(z) = ------ = ------ where z = 0
26 13
Z ~ Ber(8/13)
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