[機統] Expectations

[cecilia0305 (Cecilia)]

Let X be a random variable of the continuous type that has pdf f(x).

If m is the unique median of the distribution of X and b is a real constant,

show that E(|X-b|)=E(|X-m|)+2integral(m to b)(b-m)f(x)dx,

provided that the expectations exist.

For what value of b is E(|X-b|) a minimum?

不知該如何下筆

才剛學數統不久的@@

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 220.142.191.134
→ njru81l     :漏了x ? (b-m)xf(x)dx??
→ njru81l     :想錯了，不是 x 請無視上面那行
推 jimmy86204  :http://ppt.cc/ygqm
→ jimmy86204  :昨天剛好交完這題 人在外面紙還有丟先拍下來看看
推 jimmy86204  :這個証明結果說明了E|X-m|  m=median為最 E|X-c| c
→ jimmy86204  :屬於R 之最小值
→ cecilia0305 :挖感謝大大的精闢解說 =)))