Do you know how to integrate X squared times E to the minus X, without looking it up?

你知道怎么不查书也能求出x平方乘e到负x的积分？

When the number is 2, we say: " squared" , so: " X squared" .

当数字为 2 时， 我们说：“平方” ，所以：“X 平方” 。

This is my chi-square statistic, or we could call it a big capital X squared.

这是我的卡方统计量，或者我们可以称之为大资本 X 平方。

That one corresponds to the derivative of five X squared.

这个对应于5x²的导数。

But I'll write the x squared here.

但我会在这里写下 x 的平方。

Apolynomial, like X squared plus three, X plus five, E.G.

多项式 比如X²+3X+5 例如。

You can multiply it out and get one plus two X plus X squared.

您可以将其相乘并得到一加二 X 加 X 的平方。

But I could just write the X squareds, over here, minus the mean of X squared.

但我可以只写 X 平方，在这里，减去 X 平方的平均值。

Let's limit ourselves to polynomials, things like X squared plus three, X plus five or four x.

让我们把自己限制在多项式上 比如X²+3 x+5 4X。

Well, again, you can multiply out all the terms and get one plus three X plus three X squared plus X cubed.

好吧，同样，你可以将所有项相乘，得到一加三 X 加三 X 平方加 X 立方。

Then this term here, you have n times the mean of the x squared times m squared.

然后这里的这一项，你有 n 乘以 x 平方乘以 m 平方的平均值。

And if you solve for Y, well the top part of the circle is equal to one minus X squared to the half.

如果你求解 Y，那么圆的顶部等于 1 减去 X 的平方。

This one corresponds to the derivative of x cubed being three x squared, and after that, it'll be nothing but zeroes.

这一项对应于x³的导数为3x² 在这之后 它就是0了。

If you look at the numbers in these equations the coefficients on X and X squared and so on, well, they're actually just the numbers in Pascal's triangle.

如果你看一下这些方程中的数字，X 的系数和 X 的平方等等，嗯，它们实际上只是帕斯卡三角形中的数字。

Now, Newton is particularly interested in N equals a half because the equation for a unit circle is X squared plus Y squared equals one.

现在，牛顿对 N 等于二分之一特别感兴趣，因为单位圆的方程是 X 平方加上 Y 平方等于 1。

Take the coordinates representing the polynomial X cubed plus five, X squared, plus four, X plus five, then put those coordinates on the right of the matrix.

取表示多项式(X³+5)(X²+4)(X+5)的坐标 然后把这些坐标放到矩阵的右边。

Now to calculate chi-square statistic, we essentially just take-- let me just show it to you, and instead of writing chi, I'm going to write capital X squared.

现在要计算卡方统计量，我们基本上只需要 - 让我向您展示一下， 而不是写卡方， 我要写大写的 X 平方。

The 2nd basis function will be B, one of X equals X, then B two of X equals X, squared, then B, three of X equals x, cubed, and so on.

第二个基函数是B 1(X=X)然后是B2(X=X)平方 然后是B3(X=X)立方 以此类推。

So that's one minus X, the next term will be a plus X squared, the next one will be a minus X cubed plus X to the fourth minus X to the fifth.

所以这是 1 减 X，下一项是 1 加 X 平方，下一个将是减 X 立方加 X 的四次方减 X 的五次方。

All of that over, mean of the x's times the mean of the x's is just going to be the mean of the x's squared, minus over here you have the mean of the x squared.

所有这些都结束了，x 的平均值乘以 x 的平均值就是 x 的平方的平均值， 在这里减去 x 的平均值就是 x 的平方。