"If a woman gets breast cancer in the developing world, they has a much higher probability of dying than a woman who gets breast cancer in the developed world."

VOA: standard.2010.02.02

If you had a course in probability and statistics, then you'll find it easy to follow, but it's self-contained again.

如果你们学过统计学或者概率论,你们会比较容易理解,也需要你们独立学习

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For those of you who have had a course in probability and statistics, there will be nothing new here.

对于已经,学过概率和统计的同学来说,这堂课就没什么新鲜的了

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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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In fact, you'll find the probability of this happening 3% is only about 3 percent, of it happening just by accident.

实际上你会发现,出现这种情况的概率是，所以说他们的实验结果完全是偶然的。

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So in all probability, anyone who was associated with the hated occupying regime would be treated poorly It all seems to fit.

因此极有可能，任何一个人,与当权政府有关系的人都遭受虐待,一切看来没什么不妥。

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And in principle, I could redo this calculation for every single possible probability you could think of.

并且理论上,对于每一个可能的概率对,我们都可以进行预期收益计算

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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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I'm not going to expand on this because I can't get into-- This is not a course in probability theory but I'm hopeful that you can see the formula and you can apply it.

我不准备拓展这一部分,毕竟这节课不是概率论,但我希望你们能记住这个公式,并且学会应用

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So the probability of having an electron at the nucleus in terms of probability per volume is very, very high.

在单位体积内发现,一个电子的概率非常非常大。

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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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we have Nala and he meets this man, Rituparna, and this is where a probability theory apparently comes in.

有那勒,他遇到的这个人,叫睿都巴若那,这就到了讲概率论的时候了

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We're saying the probability of from the nucleus in some very thin shell that we describe by d r.

某一非常薄的壳层dr内,一个原子的概率,你想一个壳层时。

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I've learned that with high probability, the error is not in the first part of the program.

我从这一点得到了什么？,我得到的是错误有很大的可能。

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So again if we look at this in terms of its physical interpretation or probability density, what we need to do is square the wave function.

如果我们从物理意义或者,概率密度的角度来看这个问题，我们需要把波函数平方。

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But a real key in looking at these plots is where we, in fact, did go through zero and have this zero probability density.

是我们经历这些零值,而且有这些零概率密度,我们把它叫做节点。

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So again, we can think about the probability density in terms of squaring the wave function.

同样的，我们可以把,波函数平方考虑概率密度。

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I want to emphasize that it hasn't always been that way and that probability is really a concept that arose in the 1600s.

我想说,概率的表述并非一贯如此,这个概念成型于十七世纪

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Another important concept in probability theory that we will use a lot is expected value, the mean, or average-- those are all roughly interchangeable concepts.

概率论中另外一个常用的重要的概念是,期望值或者也叫均值,这两个概念可以互换

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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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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.

波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。

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And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.

当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。

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And the reason that they're the least sheilded is because they can get closest to the nucleus, so we can think of them as not getting blocked by a bunch of other electron, because there's some probability that they can actually work their way all the way in to the nucleus.

它们最不容易被屏蔽的原因,是因为他们可以更加接近原子，所以我们可以认为它们,最不容易被其它原子阻挡住，因为它们有一定的概率,离原子核非常近。

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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.

这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。

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So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.

个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。

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The answer is, in fact, there is zero, absolutely zero probability of finding a electron here.

实际上它在这里是为零的，在这里找到电子的概率严格等于零。

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And if we go ahead and square that, then what we get is a probability density, and specifically it's the probability of finding an electron in a certain small defined volume away from the nucleus.

我们得到的是，一个概率密度，它是，在核子周围，某个很小的,特定区域,找到电子的概率,所以它是概率密度。

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Probability density of finding an electron within that molecule in some given volume.

在分子内某空间找到,一个电子的概率密度。

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So because we're feeling a stronger attractive force from the nucleus, we're actually pulling that electron in closer, which means that the probability squared of where the electron is going to be is actually a smaller radius.

因为我们能感到来自原子核,的更强的吸引力，我们实际上会将电子拉的更近，那意味着电子运动的,概率半径是,事实上是一个更小的半径。

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I think it was the invention of probability theory that really started it and that's why I think theory is very important in finance.

我认为是概率论的诞生,真正促生了保险业,那也是为什么,我认为理论对于金融来说非常重要

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