So first, I choose a volatility randomly, from some distribution of possible volatilities 2 from to, in this case, 0.2.

来决定的一个值，所以首先我先随机选择一个浮动值，从可能的浮动值中的分布进行选择,在这个例子中就是0。

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And then I could also do a Gaussian one here, with the mean of and the standard deviation of volatility divided by 2.

然后我在这里再写一个高斯分布的函数，它的浮动值的平均值和,标准偏差值都除了2。

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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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With a different volatility for the stocks because that was also selected randomly, plus some market bias.

或者均匀分布的一个随机值,因为数值选择上的随机性，再加上市场偏好。

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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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Or it could be uniform, where every value was equally probable.

还有均匀分布，每个值都有相同的可能性。

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To actually apply this it helps to go to something called the normal approximation to the binomial, because it's kind of difficult to compute this formula.

在实际应用这些公式的时候,需要运用二项分布的正态近似定理,因为二项分布公式的值很难计算

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And then I'll create this function, d1 this distribution d 1, which will, whenever I call it, give me a random, a uniformly selected value between minus and plus volatility.

然后我会创建这个函数，这个概率分布，每次我调用这个函数的时候，他会给我返回一个随机的，按照均匀分布,从正负浮动值之间选择的值。

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I'll draw something from the distribution, so this is interesting, distribution I'm now calling self dot distribution, and remember this will be different for each stock.

我会从分布中读取一个值，这就是有趣的部分，我现在会调用self。,请记住每只股票都是不一样的。

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Then, if n = 100--now I'm going to label this x differently, I'm now going to show the normal bell-shaped curve and I'm going to do this from 0 to .4.

如果n=100,现在我得重新标x值,我现在要画正态分布的钟形曲线了,在这儿用0到0.4

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