课后讨论
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通过长时间的观察,我们得到以下统计结论。
1. 性别随机变量Sex表示校园内男生(Male)和女生(Female)的概率。
| Sex | Probability |
| Male | 0.4 |
| Female | 0.6 |
2. 性别随机变量与头发长短随机变量(Sex, Hair)的联合概率如下表所示,表示不同性别中,出现长发(Long)、短发(Short)的概率。
| Sex | Hair | Probability |
| Male | Short | 0.9 |
| Male | Long | 0.1 |
| Female | Short | 0.2 |
| Female | Long | 0.8 |
请使用贝叶斯公式,求解条件概率 P(Femal | Short)。
解:根据贝叶斯公式,
P(Femal | Short)
= ( P(Short| Female)* P(Female) )/ (P(Short| Female)* P(Female) + P(Short| Male)* P(Male))
= (0.6*0.2) / (0.6*0.2+0.4*0.9)
= 0.12/0.48
= 0.25

