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Suppose you could find 10,000 independent assets, then you could drive the uncertainty about the portfolio practically to 0.
假设你能找到一万项相互独立的资产，那么你就可以将这个投资组合的风险,降到几乎为零。
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It's like an insurance where people imagine they're insuring people's lives and they think that their deaths are all independent.
或许这有点像保险,在人寿保险中,每个人的死都被假定为相互独立的。
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The instant unlike binary search, where each instance was separate, here the instances overlap.
这个例子不像搜索二进制数，每个例子是独立的，这里的例子是相互重叠的。
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But since I can imagine my mind existing without my body, it follows that my mind and my body have to be logically distinct things.
由于我能够想象我的心灵独立于身体存在,可以推出,我的心灵,和身体在逻辑上是相互独立的
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These systems have some built-in knowledge, and they have to do some learning, but the learning pattern varies from system to system and there's a separateness to them.
这些系统拥有部分先天知识,它们能够进行一定的学习,但学习模式因系统的不同而有所变化,它们之间也是相互独立的
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One more thing, I said they're not independent, so we have to talk about the covariance between the returns.
还有，我说过它们不是相互独立的，因此我们还需要讨论两个收益率的协方差。
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This is a special case, though, because I've assumed that the assets are independent of each other, which isn't usually the case.
这是一个特例，因为我假设了,这个投资组合里的资产是相互独立的，但现实中通常都不是这样的。
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Now, I want to talk about forming a portfolio where the assets are not independent of each other, but are correlated with each other.
现在我要建立这样的一个投资组合,在这个组合里各项资产并不是相互独立的，而是相互关联的。
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If you toss a coin twice and the first experiment doesn't influence the second, we say they're independent and there's no relation between the two.
如果你抛两次硬币,第一次的结果并不影响第二次的结果,所以我们说他们是相互独立的,这两次试验没有关系
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.. If you can find assets that all have-- that are all independent of each other, you can reduce the variance of the portfolio very far.
如果你能找到这样的一些资产-,一些相互独立的资产，就能很大程度上缩小这个投资组合的方差。
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In the real world we don't have the problem that assets are independent.
在现实世界中,资产通常是不相互独立的。
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.. What I'm going to do now-- let's start out with the case where-- now it's going to get a little bit more complicated if we drop the independence assumption.
我现在要做的是-,让我们从案例开始-,接下来的情况会比刚才的复杂一点,因为我们去掉了“相互独立“这一前提假设。
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Just because it looks as though we can imagine it and just because it seems as though from the fact that we can imagine one without the other, it just won't necessarily follow that we really do have two things that are separate and not identical in the real world.
仅仅是因为我们似乎能够,想象到一个事物独立于,另一个事物存在这件事,并不能说明,在现实世界里,有这样两个,相互独立,而且不相同的事物
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That says that if you have independent probabilities, then the probability of two events is equal to the product of their probabilities.
意思是,几个相互独立的事件,其中两个事件同时发生的概率,等于他们分别发生的概率的乘积
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Suppose we had a lot of different stocks that we could put into a portfolio, and suppose they're all independent of each other-- that means there's no correlation.
假设我们现在有很多只不同的股票,可以放进我们的投资组合里，同时假设它们都是相互独立的-,也就是说它们之间没有相关性。
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.. I started out with the equally-weighted-- I was talking about stocks-- about n stocks that all have the same variance and are all independent of each other.
开始的时候我讲了等权重的-,我开始时讲了股票-,几支拥有相同方差的股票,彼此间相互独立。
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having a lot at sort of independent sort of bets.
同时下多种类别而又相互独立的赌注。
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Put the same point the other way around: If I can imagine A without B, then A and B have to be logically distinct things.
把这点推而广之,如果我可以想象A在没有B的情况下存在,那么A和B在逻辑上是相互独立的
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So, we're going to have n independent assets; they could be stocks.
假设我们有n个相互独立的资产;,假设是股票。
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There's n = 2, but not independent or not necessarily independent.
即n等于，这两项资产不是或者不一定是相互独立的。
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