“The Cartoon Guide to Statistics” promised readers they would chew over binomial distributions and conditional probability with the same ease with which they enjoyed Spider-Man.

那年一本名叫《统计学卡通指南》的书，承诺可以让读者津津有味地学习二项条件概率，像阅读《蜘蛛侠》一样轻松愉快。

What you're looking at right now, by the way, is known in the business as a binomial distribution, one of THE most fundamental distributions in probability.

顺说一下，你现在看到的被称为二项，这是概率论中最重要的之一。

So if this is a binomial distribution then this lambda would be equal to the number of trials times the probability of success per trial.

所以如果这是一个二项，那么这个λ等于试验次数乘以每次试验成功的概率。

The probability for each value is given by what's called a binomial distribution, which peaks at the most likely outcome.

每个值的概率由所谓的二项给出，该在其最可能的结果处达到峰值。

We can find out by using the binomial distribution.

我们可以通过使用二项来找出答案。

Even with just 10 trials, the curves, the normal distribution here is in purple and the binomial distribution is in blue.

仅进行10次试验，曲线图中，正态以紫色显示，而二项则用蓝色表示，两者几乎完全重叠。

Where, in this first one, we'll set up a model for the situation and start by talking about the binomial distribution.

在第一个视频中，我们将建立一个模型来描述这种情况，并从二项开始讨论。

The binomial distribution is always finite.

二项总是有限的。

And don't worry, I'm going to do a couple of more examples with this because I really want you to get the hang of the binomial distribution before we move into the normal distribution.

别担心，我将再举几个例子， 因为我真的希望你在我们进入正态之前掌握二项的窍门。

And we saw if you actually figured out the probability distribution for this random variable you get that nice binomial distribution that looks a little bit like a bell curve.

而我们看到，如果你实际计算出这个随机变量的概率，你会得到一个看起来有点像钟形曲线的漂亮的二项。

And I want to show you that as you take more and more moves the normal distribution becomes a better and better approximation for the binomial distribution.

我想向您展示的是，随着采取的步数越来越多，正态对二项的近似程度会越来越好。

But in the binomial distribution you can kind of view it that way.

但在二项中，你可以这样看待它。

If you actually then said, oh, this is a binomial distribution, so the probability that our random variable equals some given value, k.

如果你实际上说， 这是一个二项，所以我们的随机变量等于某个给定值k的概率。

And this is true only for binomial distributions.

并且这一点仅适用于二项。

So the blue line right here -- I'll trace it maybe in yellow so you can see it -- is the plot of the binomial distribution.

所以这里的蓝线——我可能会用黄色描出来以你看清楚——是二项的图像。

There's also the binomial distribution and the normal distribution, which is what some people call the Gaussian or the bell curve.

还有二项正态，有些人称之为高斯或钟形曲线。

And then, we actually calculated the expected value for the particular binomial distributions that we studied, especially the one with the flipping of the coin.

随后，我们确实计算了所研究特定二项的期望值，特别是涉及抛硬币的那个。

The mean of the binomial distribution is essentially the probability of taking a left step times the total number of trials.

二项的均值实质上等于采取左步的概率乘以试验的总次数。

The binomial distribution is a discreet probability distribution.

二项是一种离散概率。

So in a binomial distribution what is the probability-- so if I say, what is the probability that X is equal to k?

所以在二项中， 概率是多少——也是说， 如果我说，X等于k的概率是多少？