Fw: [問題] Casella and Berger 的題目
※ [本文轉錄自 Statistics 看板 #1FMjz3B5 ]
作者: rockken () 看板: Statistics
標題: [問題] Casella and Berger 的題目
時間: Sat Mar 10 12:57:36 2012
Chapter 5 的 Exercises 5.2
Suppose X1, X2 ... are jointly continuous and independent, each distributed
with marginal pdf f(x), where each Xi represents annual rainfall at a given
location
(a) Find the distribution of number of years until the first year's rainfall,
X1, is exceeded for the first time
(b) Show that the mean number of years until is exceeded for the first time
is infinite
我目前的解法
a)
因為一年中不管下雨幾天，有大於一天時，即能計算出當年的降雨量多寡。
故假設年下雨機率為 p，用幾何分配直到一年中有出現下雨時，試驗停止，
Y代表歷經年數，分配為 f(y)=p*(1-p)^(y-1) y=1,2,3.... 0<p<1
b) 幾何分配期望值為 1/p 如果 p 機率很小， 期望值變為無窮大。
可是這樣都沒用到題目中所給的 f(x) 分配??
因為沒有詳解，是我會錯題意，還是哪邊算錯，勞請大家幫我解惑一下 謝謝
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※ 編輯: rockken 來自: 114.35.198.94 (03/10 22:10)
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※ 轉錄者: rockken (114.35.198.94), 時間: 03/13/2012 23:07:11
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