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When you get--this is Rituparna, counting the leaves on a tree-- you can estimate, from a sample, the population expected values.
如果你...像数叶子的睿都巴若那一样,只有部分样本的话,你可以来估计总体均值
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We can define it in a couple of different ways depending on whether we're talking about sample mean or population mean.
我们有几种不同的方式去定义这个概念,取决于我们指的是,样本均值还是总体均值
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What we did--the core theoretical framework that we had-- was the mean variance theory, which led us to the capital asset pricing model.
我们讲到了投资组合多元化的核心理论框架,即均值-方差模型,之后又讲到了资本资产定价模型
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Jeremy says in the text that the geometric return is always lower than the arithmetic return unless all the numbers are the same.
杰里米在书里说几何平均,总是比算术平均小,当然如果所有数字都一样,两个均值相等
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If it moves a lot--either way from the mean-- then this number squared is a big number.
如果距离均值的变动很大,那么这个平方数也会很大
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One would be--I'm having a little trouble putting this into the Rituparna story, but you see the idea. You know the average, I assume.
这个1是指,我好像把这个式子,和睿都巴若那的故事弄混了,但你们应该懂我的意思,应该明白均值的概念
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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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In fact, I have it--suppose we have three assets and we want to compute the efficient portfolio frontier, the mean and variance of the portfolio.
事实上，假如我们拥有三种资产,我们想计算有效边界，及投资组合的均值和方差。
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Number of policies doesn't affect the means but it affects that standard deviation, so it becomes very collapsed and this is the basic core idea of insurance.
保单的数量并不影响其均值,但是会影响其标准差,所以这条曲线非常陡峭,而这就是保险的核心原理
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According to my calculations it was a twenty-five standard deviation event.
根据我的估算,那次波动偏离均值有25倍标准差之巨
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But, in between, if some other number, it'll be some blend of the--mean and variance of--the portfolio will be some blend of the mean and variance of the two assets.
但如果是在0和1之间的其他数值，这个投资组合的均值和方差将会是,两项资产各自的均值和方差的综合结果。
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In finance, there's often reference to another kind of average, which I want to refer you to and which, in the Jeremy Siegel book, a lot is made of this.
在金融里,我们经常提到,另外一种均值,在杰里米·西格尔的书里多次提及
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The other kind of average is called the geometric average.
这种均值叫做几何平均
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It's the truth, but there are also sample means.
这些是真实的值,但同时也有样本均值
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What is the mean?
均值是多少
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What we want to do now is compute the mean and variance of the portfolio-- or the mean and standard deviation, since standard deviation is the square root of the variance-- for different combinations of the portfolios.
我们现在要做的是,计算这个投资组合的均值和方差-,或者均值和标准差，因为标准差的平方就等于方差-,这对任何投资组合都是一样的。
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Now, underlying our theory is the idea that we measure the outcome of your investment in your portfolio by the mean of the return on the portfolio and the variance of the return on the portfolio.
而理论的基础是,我们通过计算,组合收益率的均值，和组合收益率的方差,来衡量一个投资组合的优劣。
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x1 The portfolio mean and variance will depend on x1 x1=1 in the way that if you put--if you made x1 = 1, it would be asset 1 x1=0 and if you made x1 = 0, then it would be the same as asset 2 returns.
投资组合的均值和方差取决于1,如果你令，投资组合的均值方差就与第一项资产相等1,如果你令，那么它们就会与第二项资产的参数相等。
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If x is high relative to x-bar--this is positive-- then y tends to be low relative to its mean y-bar and this is negative.
如果x比x均值要大,这个为正,而y比y均值小,这个为负
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When we have n observations it's just the summation i = 1 to n of 2/n.
当有n个观察值,这就是在i取1到n时,x减去x均值的平方,除以n的累加
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Well, the mean is always .2 no matter how many policies you write, so it's going to be--we're going to have a normal distribution centered on .2.
不论你签了多少份保单,均值永远是0.2,所以这就是一个关于x=0.2对称的,正态分布
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The mean proportion-- The mean of x/n, is equal to p.
事件发生频率的均值,即x/n的均值,就等于p
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The population mean is often written "X-bar."
总体均值一般写作X拔
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