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You can see the different points-- I've calculated this using data from 1983 until 2006-- and I computed all of the inputs to those equations that we just saw.
你可以观察不同的点-,我用从1983年到2006年的数据-,代入我们刚教授的等式,进行了计算。
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using, like, you know, pre-existing data
用的是，你知道，已经存在的数据
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So by using the tabulated data, we can really determined heats of formation for most reactions that you might contemplate, OK?
所以，使用这些表格,我们就能确定大多数,你可能碰到的反应的生成热？
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We did a study using the Framingham data ourselves several --some years ago where we were interested in the issue of weight cycling.
几年前我们用弗明汉研究的数据做过研究,我们对体重循环这个问题很感兴趣
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I mean, these are huge, huge, numbers that humans are now using to protect their data.
我的意思是它们是非常，非常巨大的，数字，用来为保护我们的数据。
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I did it myself using my data, but it would always look more or less like this-- slightly different positions if people use different estimates.
这幅图是我根据自己的数据画出来的，有效边界的图形大致就是如此-,随着人们采用不同的估计值,其位置会发生微小的变化。
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I don't find that my analysis is profound in the final answer, I just took some estimates using my data and, again, we could-- if someone wanted to argue with us they could argue with my estimates of the expected returns of the standard deviations and the covariances, but not with this theory.
我在计算过程中并没有做太深入的分析，我只是用我的数据做了一下大概的估计,我再说一次，我们可以-,如果有人想就这个问题与我们争辩,他们可以争论我对期望收益的估计,或是争论标准差和协方差的估计值，但并不会针对理论本身。
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They might say my sample period was off, ... but that's what the theory-- ... using my data for the sample period that I computed-- the expected returns and co-variances says one should do.
他们可能说我的采样周期是有问题的，不过我的结果都是靠理论-,我采用自己收集的数据计算出-,预期收益和协方差可以用来指导我们的投资行为。
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But one of the teaching fellas also passed long to us recently, a little real world example of what happens when you're not mindful of various data types and you're not mindful of the imprecision that's inherent in representing data in a computer, at least using a language like C and low level primitives like floats and even doubles.
最近有个助教告诉我们，一个现实世界中的例子,当你不注意各种各样的数据类型,也不注意在计算机中表示数据时,其内在的不精确性，至少在用像C语言,和float甚至double型数据时，那将会发生什么？
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