A particle A moves along the x-axis between 0 and 1 and particle B
moves along the y-axis between 0 and 1. The movements of particles
A and B are independent. If the location that particle A stops on
the x-axis is u1 and particle B stops on the y-axis is u2. Let X be
the area of the square(0<x<u1,0<y<u2). Let E(X) be the expected value
of X. Let M(X) be the expected value of X.
(a)Compute P( X>E(X) )
(b)Is E(X) larger than M(X)?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.139.60.2
> -------------------------------------------------------------------------- <
作者: zhuangz (築夢? 逐夢?) 看板: Statistics
標題: Re: [問題] 一題機率的問題
時間: Sun Mar 5 00:17:45 2006
※ 引述《feelingon (結束了..)》之銘言：
: A particle A moves along the x-axis between 0 and 1 and particle B
: moves along the y-axis between 0 and 1. The movements of particles
: A and B are independent. If the location that particle A stops on
: the x-axis is u1 and particle B stops on the y-axis is u2. Let X be
: the area of the square(0<x<u1,0<y<u2). Let E(X) be the expected value
: of X. Let M(X) be the expected value of X.
: (a)Compute P( X>E(X) )
: (b)Is E(X) larger than M(X)?
Does M(X) mean the median of X?
(a) E(X)=1/4 (trivial)
P(X>E(X))=P(AB>1/4)=1-P(AB≦1/4)=1-[1/4+ln(√2)]=3/4-ln(√2)
(b) To check whether P(X>E(X))<1/2, if yes, then E(X) is larger then
M(X), because P(X>M(X))=1/2 in this case.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.224.75.26
※ 編輯: zhuangz 來自: 61.224.75.26 (03/05 00:18)