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So, let's go ahead and think about drawing what that would look like in terms of the radial probability distribution.
让我们来想一想如果把它的,径向概率分布画出来是怎么样的。
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This is the radial probability distribution formula for an s orbital, which is, of course, dealing with something that's spherically symmetrical.
这个ｓ轨道的,径向概率分布公式，它对于球对称,的情形成立。
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If you follow through from the independent theory, there's one of the basic relations in probability theory-- it's called the binomial distribution.
如果继续往下看,在概率论里有一个基本的概念,叫做二项分布
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Last time we looked at the notion, last lecture we looked at the idea of a distribution.
上一次我们看过这个概念，上一次讲座中我们看到了概率分布的概念。
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It turns out that the probabilities of scoring here are as follows, 63.6, 94.4, 89.3, and 43.7.
研究的结果,概率分布如下,63.6 94.4 89.3 和 43.7
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So I mentioned you should be able to identify both how many nodes you have and what a graph might look like of different radial probability distributions.
我说过你们要能够辨认,不同的径向概率分布有多少个节点,以及它的图画出来,大概是什么样的。
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But still, when we're talking about the radial probability distribution, what we actually want to think about is what's the probability of finding the electron in that shell?
但当我们讲到径向概率分布时,我们想做的是考虑，在某一个壳层里,找到电子的概率,就把它想成是蛋壳？
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So, you should be able to generally identify and draw the general form of these radial probability distributions.
所以你们应该可以大概辨认,并且画出概率,分布的大致形式。
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Or we could just look at the radial probability distribution itself and see how many nodes there are.
或者我们可以直接,看径向概率分布图,本身看看里面有几个节点。
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This refers to random variables that have fat-tailed distributions-- random variables that occasionally give you really big outcomes.
这就表示,服从长尾分布的随机变量,这些数据出现极端值的概率比较大
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We will always have r equals zero in these radial probability distribution graphs, and we can think about why that is.
在这些径向概率分布图里,总有ｒ等于０处，我们可以考虑为什么会这样。
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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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And when we do that we can see this curve, this probability curve, where we have a maximum probability of finding the electron this far away from the nucleus.
当我们这样做时，我们可以看到这个曲线，这个概率分布曲线，这里有发现,电子的最大概率。
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Similarly, if we were to look at the radial probability distributions, what we would find is that there's an identical nodal structure.
相似地如果我们看看,径向概率分布,我们会发现有一个完全相同的波节结构。
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So, let's actually compare the radial probability distribution of p orbitals to what we've already looked at, which are s orbitals, and we'll find that we can get some information out of comparing these graphs.
让我们来比较一下ｐ轨道,和我们看过的,ｓ轨道的径向概率分布，我们发现我们可以通过,比较这些图得到一些信息。
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So we're going to assign to each stock, when we create it, a distribution.
所以我们在创建每只股票时，要给它们指定一中概率分布。
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It's somewhat different when we're talking about the p or the d orbitals, and we won't go into the equation there, but this will give you an idea of what we're really talking about with this radial probability distribution.
当我们讨论ｐ轨道或者,ｄ轨道的时候会有些不同，我们那时不会给出方程，但它会给你们一个,关于径向概率,分布的概念。
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So we talked about radial nodes when we're doing these radial probability density diagrams here.
我们画这些径向概率分布图的时候,讨论过径向节点。
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And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.
为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。
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So what we're graphing here is the radius as a function of radial probability.
我们要画的是径向概率,作为半径的函数分布。
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So here, what I'd like you to do is identify the correct radial probability distribution plot for a 5 s orbital, and also make sure that it matches up with the right number of radial nodes that you would expect.
这里，你们要辨认,哪个是５ｓ轨道的正确概率分布，并且确保它和你们,预期的节点数相符合。
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So, the example that we took on Monday and that we ended with when we ended class, was looking at the 1 s orbital for hydrogen atom, and what we could do is we could graph the radial probability as a function of radius here.
周一我们,最后讲到了，粒子是氢原子１ｓ轨道，我们可以画出,这幅径向概率分布曲线。
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So, that's a more complete quantum mechanical picture of what is going on here.
对它，更完整的描述,如果我们,假定径向概率分布。
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It uses the binomial distribution to calculate the probability of getting any specific number of accidents.
保险公司就可以用二项分布公式,来计算特定数目事故发生的概率
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That's different when you have continuous values-- you don't have P because it's always zero.
和离散型随机变量的分布不同的是,连续型随机变量的分布中,某一点的概率值始终是零
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And then I'll create this function, d1 this distribution d 1, which will, whenever I call it, give me a random, a uniformly selected value between minus and plus volatility.
然后我会创建这个函数，这个概率分布，每次我调用这个函数的时候，他会给我返回一个随机的，按照均匀分布,从正负浮动值之间选择的值。
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There's a distribution of how it would move.
它的改变是有概率分布的。
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So, we can look at other radial probability distributions of other wave functions that we talked about.
我们可以来看一看我们讨论过的,其它一些波函数的径向概率分布。
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OK. So let's actually go to a clicker question now on radial probability distributions.
好，让我们来做一个关于,径向概率分布的题目。
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We'd started on Monday talking about radial probability distributions for the s orbitals.
我们从星期一开始讨论了,ｓ轨道的径向概率分布。
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