推 lily84627:謝謝:) 11/26 01:50
應該是這樣@@
r N-r
( ) ( )
超幾何機率分配 p(y)= _y_____n-y______
N
( )
n
r1 N-r1 r2 N-r2
p(y|r1)/p(y|r2) = ( ) ( ) ( ) ( )
_y___n-y__ / _y___n-y__
N N
( ) ( )
n n
= r1!(r2-y)!(N-r1)!(N-r2-n+y)!
____________________________
r2!(r1-y)!(N-r2)!(N-r1-n+y)!
r1 N-r1 r2 N-r2
p(y+1|r1)/p(y+1|r2) = ( ) ( ) ( ) ( )
_y+1___n-y-1__ / _y+1___n-y-1__
N N
( ) ( )
n n
=r1!(r2-y-1)!(N-r1)!(N-r2-n+y+1)!
_______________________________
r2!(r1-y-1)!(N-r2)!(N-r1-n+y+1)!
p(y|r1)/p(y|r2) (r2-y)!(N-r2-n+y)!(r1-y-1)(N-r1-n+y+1)!
________________________ = _________________________________________
p(y+1|r1)/p(y+1|r2) (r1-y)!(N-r1-n+y)!(r2-y-1)!(N-r2-n+y+1)!
(r2-y)(N-r1-n+y+1)
= ____________________ > 1
(r1-y)(N-r2-n+y+1)
∴p(y|r1)/p(y|r2) > p(y+1|r1)/p(y+1|r2)
※ 引述《lily84627 (chang)》之銘言：
: 不好意思冒昧請問一題統計學。
: 題目如下:
: r N-1
: ( ) ( )
: 超幾何機率分配 p(y)= _y_____n-y______
: N
: ( )
: n
: write p(y) as p(y|r). Show that if r1 < r2 then
: p(y|r1)/p(y|r2) > p(y+1|r1)/p(y+1|r2)
: 我了解超幾何分配也了解條件機率可是此題卻完全不知如何著墨，感謝大家的相助.
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