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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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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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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minus volatility to plus volatility it will return any value in here.

浮动值到+浮动值之间等概率地,去返回一个值。

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In order to compute using this formula you have to know the true probabilities.

使用这些公式之前,必须知道真实的概率值是多少

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You can also have angular notes, and when we talk about an anglar node, what we're talking about is values of theta or values of phi at which the wave function, and therefore, the wave function squared, or the probability density are going to be equal to zero.

我们也可以有角向节点，当我们说道一个角向节点时，我们指的是在某个theta的值,或者phi的值的地方，波函数以及波函数的平方，或者概率密度等于零。

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I'm plotting--this is the probability of various values of x/n.

这里是x/n等于各个值的概率

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