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单词 Binomial coefficients
释义

Binomial coefficients

原声例句
可汗学院:统计学(视频版)

And then we need to figure out the binomial coefficient.

然后我们需要计算出二项式系数。

可汗学院:统计学(视频版)

And then you need to know that you needed the binomial coefficient.

然后你需要知道你需要二项式系数。

可汗学院:统计学(视频版)

And this is neat because it calculated the binomial coefficients.

这很简洁,因为它计算了二项式系数。

可汗学院:统计学(视频版)

So I'm just going to express the binomial coefficient expression in Excel.

所以我只是打算在Excel中表达二项式系数表达式。

可汗学院:统计学(视频版)

So let's write out the binomial coefficient and see if we can do something there.

所以让我们写出二项式系数,看看我们是否可以在那里做点什么。

可汗学院:统计学(视频版)

And actually, let me write this in terms of a binomial coefficient.

实际上,让我用二项式系数来写这个。

可汗学院:统计学(视频版)

The limit as n approaches infinity-- let me write out this binomial coefficient.

n 接近无穷大时的极限——让我写出这个二项式系数。

可汗学院:统计学(视频版)

And so this is why it's even called the binomial coefficient.

这就是为什么它甚至被称为二项式系数的原因。

可汗学院:统计学(视频版)

And then you multiply it times the binomial coefficient.

然后将它乘以二项式系数。

可汗学院:统计学(视频版)

But if you think about it that way, the binomial coefficient kind of starts to make sense.

但如果你这样想,二项式系数就开始有意义了。

可汗学院:统计学(视频版)

But we did still use the binomial coefficient.

但是我们仍然使用二项式系数。

可汗学院:统计学(视频版)

And I did that to just show you that this is the binomial coefficient on this term.

我这样做只是为了告诉你这是这个词的二项式系数。

可汗学院:统计学(视频版)

But I just wanted to show you that we're still using the binomial coefficients.

但我只是想告诉你我们仍在使用二项式系数。

可汗学院:统计学(视频版)

Each of the values of probabilities for each of the random variable values-- you can figure them out by using your binomial coefficients.

每个随机变量值的每个概率值——您可以使用二项式系数计算出它们。

可汗学院:统计学(视频版)

But if you watch those or if you have a little bit of experience with this, you would recognize that this is the binomial coefficient.

但是如果你看过那些或者你对此有一点经验,你会认识到这是二项式系数。

可汗学院:统计学(视频版)

And just so that we make it clear and connect it all to the binomial distribution, if we were to have done the n choose 0 here, what's the binomial coefficient?

为了让我们弄清楚并将其全部连接到二项式分布, 如果我们在这里完成 n 选择 0,那么二项式系数是多少?

可汗学院:统计学(视频版)

I encourage you to review the videos I made in the probability playlist on binomial coefficients, and on this flipping of coins type of probability problems because I go a little more in detail in the actual intuition of this.

我鼓励您查看我在概率播放列表中制作的关于二项式系数的视频,以及关于这种抛硬币类型的概率问题, 因为我在实际直觉中更详细地介绍了这一点。

中文百科

二项式系数 Binomial coefficient

(重定向自Binomial coefficients)
二项式系数可排列成杨辉三角形。
帕斯卡三角形的第1000行,垂直排列,且以灰阶表示系数的十进制数字,向右对齐,故左边边界约是二项式系数的对数,图中可见数族形成一对数凹数列。
Hay 5×4×3 formas de escoger ordenadamente tres objetos de un conjunto con cinco.

二项式系数在数学上是二项式定理中的系数族。其必然为正整数,且能以两个非负整数为参数确定,此两参数通常以nk代表,并将二项式系数写作\tbinom nk ,亦即是二项式幂(1 + x)的多项式展式中,x项的系数。如将二项式系数的n值顺序排列成行,每行为k值由0至n列出,则构成帕斯卡三角形。

此数族亦常见于其他代数学领域中,尤其是组合数学。任何有n个元素的集合,由其衍生出拥有k个元素的子集,即由其中任意k个元素的组合,共有\tbinom nk个。故此\tbinom nk亦常读作「n选取k」。二项式系数的特性使表达式\tbinom nk的定义不再局限于nk均为非负整数及kn,然此等表达式仍被称为二项式系数。

英语百科

Binomial coefficient 二项式系数

(重定向自Binomial coefficients)
The binomial coefficients can be arranged to form Pascal's triangle.
Visualisation of binomial expansion up to the 4th power
1000th row of Pascal's triangle, arranged vertically, with grey-scale representations of decimal digits of the coefficients, right-aligned. The left boundary of the image corresponds roughly to the graph of the logarithm of the binomial coefficients, and illustrates that they form a log-concave sequence.

In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written \tbinom nk. It is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x). Under suitable circumstances the value of the coefficient is given by the expression \tfrac{n!}{k!\,(n-k)!}. Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle.

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更新时间:2025/6/20 21:52:20