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# 等可能概型 | ||
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?> 非常惭愧地说,这次上课我睡得相当的好。不是半睡半醒的挣扎状态,是完全睡着了。 | ||
>我也记不到讲到哪里了,大约的确还没有讲到贝耶斯,那么应该是仅仅讲完了等可能概型和一部分条件概率吧。那么今天先把等可能概型写了,然后写电路原理的笔记,最后写模拟电路的(模拟电路依靠星期一下午把笔记写全,上课效率果然还是不错的。) | ||
## 古典概型 | ||
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随机试验具有两个特点,那么这样的随机试验概率模型就是古典概率模型: | ||
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- 试验只有有限个可能结果 | ||
- 每个可能结果在试验中出现的可能性相等。 | ||
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*我这里应该出现了一个认识误区。我之前一直认为基本事件都是等可能的,但是仔细回顾基本事件的定义,可以发现基本事件的定义并没有这样的意思。并且还有“等可能基本事件的说法,这些都说明基本事件不见得是等可能的。”* | ||
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下面这个概率就叫做古典概率 | ||
$$ | ||
P(A) = \frac{k}{n} = \frac{\Alpha中的样本点数}{\Omega中的样本点数} | ||
$$ | ||
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古典概率的计算方法是计数,较为复杂的计数基本方法是排列与组合,有对应了两个基本的摸球模型: | ||
1. 每次取一个球,取出来的球是有序的。 | ||
1. 有放回抽取,总的样本点数是$N^\gamma$ | ||
2. 不放回抽取,总样本点数是$P^{\gamma}_{N} = N(N-1)...(N-r+1)$ | ||
2. 一次取$N$个球,取出来的球是无序的。用组合数表示。于是有超几何概率,表示的是取出的球中恰有$k$个某个颜色的球的概率。 | ||
$$ | ||
p_k = \frac{C^k_mC^{n-k}_{N-m}}{C^n_N}, k = 0,1,...,m. | ||
$$ | ||
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>然后书上有一些例题,我的评价是我现在没精神做题。后面对本章做总结时必须专门写习题篇。 | ||
## 几何概型 | ||
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>其实说起来都是高中学过的对不? | ||
**一个随机试验,若所有可能结果“等可能”地出现在一个有界的欧氏区域$\Omega$内,则称这个试验的概率模型为几何概型。** | ||
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>注意到谈及概型都是针对随机试验来讲的,是“随机试验的概率模型”。 | ||
这一部分没有过多的什么。能有什么呢?很多都是高中的知识,难搞的都在后面。 | ||
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!>作业做了吗?或者说课后习题做了吗?没有做快去做,我都这么懒了还是打算先把概统这两节的习题做了再开始写《电路原理》的课堂笔记。 |
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# 条件概率及派生的三个公式 |