※ [本文轉錄自 Math 看板 #1YfReMno ]
作者: Qdream (宅男科學家) 看板: Math
標題: [機統] 常態分配問題
時間: Sun Jun 12 18:04:02 2022
大家好：
在寫Ross A First Course in Probability的習題時遇到問題，
想請教各位，謝謝!
題目如下：
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?
題目中提到當α值是多少的時候，犯錯的機率會相等，這裡是指把白認成黑，
把黑認成白嗎？但是題目又說不管最後判斷是黑或是白？
在網路上看到有人問過，但是對於底下的作法就不是太懂
(縮網址 https://reurl.cc/e37Omm )
P(該點來自黑色區域|資料值為5)=P(該點來自白色區域|資料值為5)
這樣假設就能夠代表犯錯的機率會相等嗎？
麻煩板友了，謝謝！