We can find out by using the binomial distribution.

我们可以通过使用二项分布来找出答案。

It's the simplest case of the binomial distribution.

这是二项分布最简单的情况。

And we said, OK, we wanted to model it as a binomial distribution.

我们说，好的，我们想把它建模为一个二项分布。

So just finishing up with our binomial distribution, n moments, choose k successes times the probability of success.

所以二项分布的计算就是，在n试验k功的概率。

“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分布和条件概率，就像阅读《蜘蛛侠》一样轻松愉快。

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分布给出，该分布在其最可能的结果处达到峰值。

So in any binomial distribution this is a probability that you get k successes.

因此，在任何二项分布，这就是你获得k功的概率。

The binomial distribution is a discreet probability distribution.

二项分布是一种离散概率分布。

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，我们将建立一个模型来描述这种情况，并从二项分布开始讨论。

Why is this called a binomial distribution?

为什么这被称为二项分布？

And why this is called the binomial distribution.

以及为什么这被称为二项分布。

So this is why it's called a binomial distribution.

所以这就是它被称为二项分布的原因。

But now, let's prove it to ourselves that this is really true for any a random variable that's described by a binomial distribution.

但现在，让我们自己证明这一点， 对于任何服从二项分布的随机变量， 这确实是正确的。

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

所以在二项分布， 概率是多少——也就是说， 如果我说，X等于k的概率是多少？

You would actually get a binomial distribution where you'd get a bunch of bars like that.

实际上，你会得到一个二项分布，其会出现许多像那样的条形。

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分布，那么这个λ就等于试验数乘以每试验功的概率。

In the binomial distribution, you say, oh, what is the probability of getting a 5?

在二项分布， 你说， 哦，得到5的概率是多少？

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.

顺便说一下，你现在看到的被称为二项分布，这是概率论最重要的分布之一。

So you assume that a lot of things have-- well, in the discreet case, a binomial distribution.

所以你假设很多东西都有——嗯，在谨慎的情况下， 二项分布。

So you could literally look at every combination of getting 150 households from this, and you would actually get a binomial distribution.

因此，你可以实际考虑从这组数据抽取150户家庭的每一种组合，结果实际上会得到一个二项分布。