Re: [理工] [機率]-結合機率
※ 引述《wolf0000 (小狼)》之銘言：
: Given three independent random variables,each uniformly distributed over
: the interval 0 to 1. What is the probability that they are within a distance
: of 1/2 of each other?
: 請問這題該怎麼思考? 3個變數的joint機率好容易搞混....
: 答案是1/2。
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我覺得應該要定義好何謂 distance
不同的 metric space 下
會有不同的機率統計特性
例如 d(X,Y) ≡│X - Y│
d(X,Y) ≡ √(X^2+Y^2)
題目應該是 把距離定義成: d(X,Y) ≡│X - Y│
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∫∫∫ f(X=x,Y=y,Z=z) dx dy dz
V
= ∫∫∫ f(X=x)*f(Y=y)*f(Z=z) dx dy dz
V
= ∫∫∫ dV
V where V:{ (x,y,z)│ |x-y|≦(1/2)
& |y-z|≦(1/2)
& |z-x|≦(1/2)
, x、y、z 屬於 R }
( 令 (u,v,w) = ( x-y , y-z , z-x ) )
1/2 1/2 1/2
= ∫ ∫ ∫ (1/2) du dv dw
-1/2 -1/2 -1/2
= 1/2
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