Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [mixing-variables]

The tag has no usage guidance.

0
votes
1answer
17 views

Expressing a CDF with positive support as a mixture of two components

Consider the two-component mixture $$ F(z)=\lambda F_1(z)+(1-\lambda)F_2(z) $$ where all the $F$'s are CDFs and $\lambda\in [0,1]$. A1: Assume that $F(z)=0$ $\forall z\leq 0$. Claim: A1 implies ...
-1
votes
1answer
27 views

Demonstration of an equivalence between a function a limit. [closed]

Given f(x)={0 if x is irrational and 1 if x is rational} How do I prove the following equality is true? :
0
votes
0answers
45 views

Why are dependent (predicted) variables replicating one of the explanatory variables?

In a multiplie regression problem, I have 3 different explanatory variables X1, X2, X3 that try to explain variations in the dependent variable Y. The result (Y) is always almost the same as one of ...
0
votes
1answer
32 views

Function needed when combining two variables

I would like some suggestions of functions to solve a problem. I need to construct a function of two variables, where the lower limit of this variables are 0 and the upper one is 100. And the ouput ...
2
votes
1answer
77 views

Overview of the different types of mixing sequences

I have come across the terms strong mixing, $\alpha$-mixing, $\beta$-mixing, $\phi$-mixing, $\rho$-mixing. Could somebody please compile an answer that would summarize their definition in some clear ...
11
votes
1answer
422 views

prove this inequality with $63$

Let $x,y,z,w>0$, and such $x^2+y^2+z^2+w^2=1$. show that $$x+y+z+w+\dfrac{1}{63xyzw}\ge\dfrac{142}{63}\tag{1}$$ I know $$x^2+y^2+z^2+w^2\ge 4\sqrt[4]{x^2y^2z^2w^2}\Longrightarrow xyzw\le \dfrac{...
0
votes
1answer
53 views

Independence of function of random variables

I have the following question. Let $X$ and $Y$ independent random variables. We define $ Z \equiv X + Y$ and $W \equiv X/Y $ Are $Z$ and $W$ independent and how can I prove it? Thanks
-1
votes
1answer
36 views

What is the value of $a-b$ when $a$ and $b$ are constants

The expression $x^2-k^2$ where $k$ is a constant is equivalent to the expression $(x+a)(x-b)$ where $a$ and $b$ are constants. What is the value of $a-b$?
0
votes
0answers
34 views

3D graph out of two 2D graphs

I have the following two graphs: $$f(x)=(43700 - x)/2$$ $$g(y)=-16150 + 100 y - 2 (-19000 + 100 y)$$ The functions $f$ and $g$ show the liquidation price of a margin trading position for a commodity ...
0
votes
1answer
39 views

Defining variables for optimization problem

I'm defining variables for a linear programming problem, where I've already defined $x_{kj}\in\mathbb{Z}^+$. I'd like to define $$y_{kj}=\begin{cases} 1 & x_{kj}\geq 1\\ 0 & x_{kj}=0 \end{...
2
votes
1answer
66 views

Example of a distribution that is ergodic but not $\phi$-mixing?

The book "asymptotic theory for econometricians" ststes the theory that if a stationary sequence is alpha or phi mixing, it is also ergodic, but not the other way around. However, when I look at the ...
-1
votes
1answer
247 views

Gaussian mixture: zero correlation implies independence?

Consider two random vectors $X\equiv(X_1, X_2),Y\equiv(Y_1, Y_2)$ distributed as below 1) $X\sim N(\begin{pmatrix} \mu_{X,1}\\ \mu_{X,2}\\ \end{pmatrix}, \begin{pmatrix} v_{X,1} & 0\\ 0 & v_{...
4
votes
4answers
127 views

Find all the natural solutions of (a+b+c)a-3bc=0

I was trying to solve a geometry puzzle when I came across a simple algebraic problem that I couldn't solve. Given the expression $(a+b+c)a - 3bc = 0$, find all natural solutions for $a$, $b$ and $...
0
votes
1answer
133 views

Find the minimize value of $P=\sum_{cyc}\frac{1}{\sqrt{a^2+b^2}}$

For non-negative numbers $a$, $b$ and $c$ such that $ab+bc+ca=1$ find the minimize value of $$P=\frac{1}{\sqrt{a^2+b^2}}+\frac{1}{\sqrt{b^2+c^2}}+\frac{1}{\sqrt{c^2+a^2}}$$ By C-S: $\left(\sqrt{a^2+...
15
votes
4answers
689 views

How prove this $x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$

Question: let $x,y,z>0$ and such $xyz=1$, show that $$x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$$ My idea: use AM-GM inequality $$x^3+x^3+1\ge 3x^2$$ $$y^3+y^3+1\ge 3y^2$$ $$z^3+z^3+1\ge 3z^2$$ so $$2(...