→ NiceKitty:謝謝大大喔^^ 01/13 23:55
※ 引述《NiceKitty (想要有個依靠><)》之銘言：
: Let X1and X2 be independent and uniformly U(0,1), distributed.
: Ler Y= min (X1,X2), Z=max(X1X2)
: (a) Find the joint distribution of Y and Z
: (b) Find the conditional density of Z given Y=y
a.參見順序統計量的公式
2!
f(y,z)=---(z-y)^(2-2)=2 , 0<y<z<1
0!
b. F(y)=P(Y<=y)=P(min(X1,X2)<=y)=1-P(min(X1,X2)>y)=1-(1-y)^2 , 0<y<1
=>f(y)=2(1-y) , 0<y<1
f(z,y) 2 1
∴f(Z|Y=y)=--------=--------=------- , 0<y<z<1
f(y) 2(1-y) (1-y)
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