作者ShadoxFish (SX)
看板Statistics
標題[問題] 連續隨機變數問題
時間Mon Jan 26 23:10:02 2015
在Hogg的數統課本中
第一章 第五節 隨機變數 的範例二
以下節錄原文
Consider the following simple experiment: choose a real number at random from
the interval (0, 1). Let X be the number chosen. In this case the space of X i
s D = (0, 1). It is not obvious as it was in the last example what the induced
probability Px is. But there are some intuitive probabilities. For instance,
because the number is chosen at random, it is reasonable to assign
Px[(a, b)] = b - a, for 0<a<b<1.
It follows that the pdf of X is
fx(x) = 1, 0<x<1
0, elsewhere.
想請問Px[(a, b)] = b - a 是怎麼得出的，他說很直覺可是我覺得一點都不直覺…
請各位神人為我解惑QQ
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※ 編輯: ShadoxFish (114.43.104.175), 01/27/2015 00:49:15
1F：→ lenux: 面積的概念？ 01/27 03:56
2F：→ bowin: Xi值的可能範圍為(0,1), 則觀察值落在(a,b)的pdf即為 01/27 07:57
3F：→ bowin: (b-a)/(1-0)=b-a. 01/27 07:58
4F：→ bowin: 由此也可知將上述b-a視為機率Px值是合理的. 01/27 08:00