作者Qdream (宅男科学家)
看板Grad-ProbAsk
标题[理工] [机统] 常态分配问题
时间Sun Jun 12 18:05:25 2022
※ [本文转录自 Math 看板 #1YfReMno ]
作者: Qdream (宅男科学家) 看板: Math
标题: [机统] 常态分配问题
时间: Sun Jun 12 18:04:02 2022
大家好：
在写Ross A First Course in Probability的习题时遇到问题，
想请教各位，谢谢!
题目如下：
An image is partitioned into two regions, one white and the other black. A
reading taken from a randomly chosen point in the white section will give a
reading that is normally distributed with μ=4 and σ^2=4, whereas one taken
from a randomly chosen point in the black region will have a normally
distributed reading with parameters (6,9). A point is randomly chosen on the
image and has a reading of 5. If the fraction of the image that is black is α
, for what value of α would the probability of making an error be the same,
regardless of whether one concluded that the point was in the black region or
in the white region?
题目中提到当α值是多少的时候，犯错的机率会相等，这里是指把白认成黑，
把黑认成白吗？但是题目又说不管最後判断是黑或是白？
在网路上看到有人问过，但是对於底下的作法就不是太懂
(缩网址
https://reurl.cc/e37Omm )
P(该点来自黑色区域|资料值为5)=P(该点来自白色区域|资料值为5)
这样假设就能够代表犯错的机率会相等吗？
麻烦板友了，谢谢！
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※ 转录者: Qdream (223.137.246.161 台湾), 06/12/2022 18:05:25