# Questions tagged [mean]

The mean tag has no usage guidance.

**2**

votes

**1**answer

63 views

### Independence of r.v.'s following a distribution that is the ratio between complex Gaussian and Chi-square r.v.'s

Given the following two R.V.s
$$z_1 = \frac{x_1}{|x_1|^2 + |x_2|^2 + \cdots + |x_M|^2}$$
and
$$z_2 = \frac{x_2}{|x_1|^2 + |x_2|^2 + \cdots + |x_M|^2}$$
where $x_i \sim \mathcal{CN}(0,a), \forall i$...

**1**

vote

**1**answer

63 views

### Correlation between r.v.'s following a distribution that is the ration between complex Gaussian and Chi-square r.v.'s

Given the following two R.V.s
$$z_{1} = \frac{x_{1}}{|x_{1}|^2 + |x_{2}|^2 + ... + |x_{M}|^2}$$
and
$$z_{2} = \frac{x_{2}}{|x_{1}|^2 + |x_{2}|^2 + ... + |x_{M}|^2}$$
where $x_{i} \sim \mathcal{CN}(...

**1**

vote

**0**answers

27 views

### Mean and correlation of product of two random processes

I have two random process:
$$A(at)$$
$$\cos(2\pi f_0t+\Phi)$$ with these hypothesis:
$a$ and $f_0$ are constant
$\Phi$ is uniformly distributed in $[0,\pi)$
$A(at)$ is WSS
I must calculate the ...

**0**

votes

**1**answer

144 views

### The Euler's totient function and the product of distinct primes dividing $n$ versus the Heronian means

For integers $n\geq 1$ with $$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\p\text{ prime}}}p$$ we denote the squarefree kernel or radical of an integer $n$ (see if you want this Wikipedia). And $\...

**3**

votes

**1**answer

95 views

### Geometric mean of positive measures

Let me given with an obvious example. Let $\Omega\subset{\mathbb R}^n$ be an open domain. If $f,g\in L^1(\Omega)$ and $f,g\ge0$, then $\sqrt{fg}\,\in L^1(\Omega)$.
Now let me replace the absolutely ...