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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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So first, I choose a volatility randomly, from some distribution of possible volatilities 2 from to, in this case, 0.2.
来决定的一个值，所以首先我先随机选择一个浮动值，从可能的浮动值中的分布进行选择,在这个例子中就是0。
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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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He found a distribution. And, if you look more closely at the distribution, here is what he found.
他发现了分布，如果你仔细观察电荷分布的话，这就是他发现的。
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You can see that the dash distribution I drew has more out in the tails, so we call it fat-tailed.
你们可以看到,虚线画的这个分布,尾部要长很多,所以我们叫它长尾分布
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A lot more of you chose numbers between 20 and 30, so we're really getting into the meat of the distribution.
有很多人选了20至30之间的数,所以我们已经涉及到分布的问题了
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So it's generally called distribution code and whereas for the previous problems that you pretty much started from scratch, blank files you opened up nano and there was nothing there unless you put it there.
它一般被称作分布码，然而,对于之前几乎要从头做起的问题,在空白文件中什么都没有,除非你在里面写入些东西。
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Let me quickly mention there's a fairly typical grade distribution for the overall grades of this, at the end of the semester.
让我快速说说公平的评分分布,对于这整个分数，在学期结束时。
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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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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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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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These are the tails of the distribution, this is the right tail and this is the left tail.
这里是这个分布的尾部,这是右尾,这是左尾
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Sudoku And then Sudoku we did last year where it actually becomes a little more interesting where we start providing students not with a blank slate, but with some distribution code.
我们去年做的,实际上更有意思,我们给学生的不是一块白板，而是一些分布式代码。
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It will return me some random value from either the Gaussian or the normal distribution.
它会给我,返回符合高斯分布。
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In order to explain it-- I had to write down the binomial distribution to explain it properly.
要解释这一点,我要先在黑板上写一个二项分布,以便于解释清楚这个问题
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So, the question then is what is the spatial distribution of charge inside the atom?
因此，接下来的问题是,原子内部的电荷,在空间如何分布？
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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, what do we know about spatial distribution?
关于空间分布，我们了解哪些东西？
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This is called the normal distribution or the Gaussian distribution-- it's a continuous distribution.
这就是正态分布,也叫做高斯分布,这是一个连续分布
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Maybe they didn't write down the binomial distribution, but they explained the idea of insurance and it didn't sound right to the typical nineteenth century American woman.
也许他们并不会给客户写二项分布函数,但会向他们灌输保险的理念,但这看起来对19世纪的美国女性,并不奏效
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It could be that a random distribution-- I don't have colored chalk here I don't think, so I will use a dash line to represent the fat-tailed distribution.
这是一个随机分布,这里没有彩色粉笔,我就用虚线,来表示长尾分布
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The grade distribution: all right, so this is the rough grade distribution.
有关分数的分布,我介绍下大体的分数的分布
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So we're going to assume even distribution of voters on the line.
我们假设选民在线上平均分布
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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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So the test on the left, you'll remember, was the one with test one, I believe, was the uniform distribution, and test two is the Gaussian.
所以左边的测试，你得记得就是均匀分布,而第二个测试是高斯分布。
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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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For a couple of reasons. In some ways, this would be nicer, do expected cases, it's going to tell you on average how much you expect to take, but it tends to be hard to compute, because to compute that, you have to know a distribution on input.
关注最快的情况，在某种意义上来说，因为一些原因这样想挺不错的，当我们处理一个给定的问题,计算平均时间的时候,是很难计算的，因为你并不知道输入的分布情况,这些输入会是怎么样的呢？
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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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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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