作者ShadoxFish (SX)
看板Statistics
标题[问题] 连续随机变数问题
时间Mon Jan 26 23:10:02 2015
在Hogg的数统课本中
第一章 第五节 随机变数 的范例二
以下节录原文
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.
想请问Px[(a, b)] = b - a 是怎麽得出的，他说很直觉可是我觉得一点都不直觉…
请各位神人为我解惑QQ
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※ 编辑: ShadoxFish (114.43.104.175), 01/27/2015 00:49:15
1F：→ lenux: 面积的概念？ 01/27 03:56
2F：→ bowin: Xi值的可能范围为(0,1), 则观察值落在(a,b)的pdf即为 01/27 07:57
3F：→ bowin: (b-a)/(1-0)=b-a. 01/27 07:58
4F：→ bowin: 由此也可知将上述b-a视为机率Px值是合理的. 01/27 08:00