But they're accountable and we can list all possible values when they're discrete and form a probability weighted average of the outcomes.

但随机变量是离散的话,我们可以把所有的可能值列出来,然后算出加权平均值

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This refers to random variables that have fat-tailed distributions-- random variables that occasionally give you really big outcomes.

这就表示,服从长尾分布的随机变量,这些数据出现极端值的概率比较大

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That's different when you have continuous values-- you don't have P because it's always zero.

和离散型随机变量的分布不同的是,连续型随机变量的分布中,某一点的概率值始终是零

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If you have an experiment and the outcome of the experiment is a number, then a random variable is the number that comes from the experiment.

如果你有一个试验,这个试验的结果是一个数,那么相对应的随机变量,指的就是这个试验结果所对应的那个数

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We have instead what's called a probability density when we have continuous random variables.

所以我们用概率密度的概念来描述,连续型随机变量的情况

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We often assume in finance that random variables, such as returns,are normally distributed.

金融学中我们常假设随机变量,例如收益率,是服从正态分布的

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You have discrete random variables, like the one I just defined, or there are also--which take on only a finite number of values-- and we have continuous random variables that can take on any number of values along a continuum.

就像刚定义的,是一个离散型随机变量,随机变量还可以有无限种取值,也就是连续型随机变量,随机变量可以取某一区间的一切值

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Covariance is--we'll call it--now we have two random variables, so cov... I'll just talk about it in a sample term.

协方差是...我们有两个随机变量,x和y的协方差是,从样本的角度来说

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I have it down that there might be an infinite number of possible values for the random variable x.

对于这个随机变量X,可能的取值个数是无限的

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The basic definition-- the expected value of some random variable x--E--I guess I should have said that a random variable is a quantity that takes on value.

最基本的定义,某一个随机变量X的期望值E,我应该提到过,随机变量是一个可以取值的数

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F is the continuous probability distribution for x.

是x的连续型随机变量的概率分布

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