Download Mu. The simplest and easiest way to get Mu is via the official installer for Windows or Mac OSX (we no longer support 32bit Windows). We also have an experimental AppImage for Linux users running on Intel based hardware. The current recommended version is Mu 1.2.0.

2025年2月1日 · The paper "Fine Structure of Harmonic Measure" (available at https://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=980&option_lang=eng) by Makarov frequently uses the notation $\mu_1\asymp\mu_2$, for two harmonic measures $\mu_1,\mu_2$ defined on the same set, without ever

To perform a hypothesis test for $\mu_1-\mu_2$, enter $H_0$ and $H_a$. Specify the null and alternative hypotheses with the drop-down boxes. The critical value, rejection region, test statistic, and $p-$value are computed and graphed.

2021年5月1日 · let $\mu_1$ and $\mu_2$ be the two measures on $\mathbb R$ such that $\mu_1((a,b))= \mu_2((a,b))$ where $a,b \in \mathbb{R}$ for which $\mu_{1}(\{ a\})=0$, $\mu_{1}(\{ b\})=0$, $\mu_{2}(\{ a\})=0$, and $\mu_{2}(\{ b\})=0$.

MRS1，2是 效用函数 某点 (a,b)的切线斜率dx2/dx1。 U (x_1, x_2) = u_0, (fixed). By the implicit function theorem， \frac {d x_2} {d x_1} = - \frac {\partial_ {x_1}U (x_1, x_2)} {\partial_ {x_2} U (x_1, x_2)} . 知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。

$$f(x,y|\mu_1,\mu_2,\sigma_1,\sigma_2,\rho)=\frac{1}{2\pi\sigma_1\sigma_2\sqrt{1-\rho^2}}exp\left\{-\frac{1}{2(1-\rho^2)}\left[\fra...

莫比乌斯反演是数论中的重要内容。 对于一些函数 ，如果很难直接求出它的值，而容易求出其倍数和或约数和 ，那么可以通过莫比乌斯反演简化运算，求得 的值。 开始学习莫比乌斯反演前，需要先学习一些前置知识： 数论分块 、 狄利克雷卷积。 为莫比乌斯函数，定义为. 详细解释一下： 令 ，其中 为质因子，。 上述定义表示： 当任意 ，都有 时，，也就是说每个质因子都仅仅只出现过一次时，即 ， 中个元素唯一时， 等于 的 次幂，此处 指的便是仅仅只出现过一次的质因子 …

2025年2月14日 · A measurable function $f$ is $\mu_i$-integrable for $i=1$ and $i=2$ if and only if $f$ is $\mu$-integrable, and then (2.7.1) holds. My try: 1.I have proved that this true for simple function.

$$W_i=X_i-Y_i \sim N(\mu_1 - \mu_2, 2 \sigma^2)$$ n independent random variables and use it to show that $\bar{W} = \bar{X} - \bar{Y} $ is sufficient to the mean. Is that correct? Thanks

2019年4月12日 · Suppose I have three independent groups, with mean $\mu_1,~ \mu_2,~\mu_3$ respectively. How can I test whether $\mu_1 < \mu_2 <\mu_3$ or not using $n_1,~n_2,~n_3$ samples from each group? I wish to know some general methodology, not detailed calculation. I couldn't figure out how to set my hypothesis $H_0$ and $H_1$.