# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### Let W = X1/(X1+X2), how to prove **W** has a beta distribution?

I am confused when I come across this question, could anyone help? Thanks! Let X1 and X2 have independent gamma distributions with parameters α, θ and β and θ respectively. Now we let W = X1/(X1+X2), ...
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### How do mathematicians come up with beautiful equations [closed]

In Linear regression for example, we can find weights as following: $\hat{\beta}=(X^{T}X)^{-1}X^{T}y$ how someone invented this? I mean how do they transform a problem to such an equation. And ...
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### Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
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### Proving a degree sequence satisfy Chvatal’s criterion

How can I prove that a degree sequence satisfy Chvatal’s criterion? I know that i must prove that sequence A is Hamiltonian if and only if A' is hamiltonian but i am lost on where i should start. for ...
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### how to construct non-Hamiltonian graphs

I have been asked to construct a hamiltonian graph and a non-hamiltonian graph using the same degree sequence. I have had no problem constructing the hamiltonian graph however I am finding it ...
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### Min problem by using Lagrange method

$$\min x^2+y^2$$ $$\text{s.t.}\ \ (x-2)^2+(y-3)^2\le 4 \ \ \ \text{and} \ \ \ x^2=4y$$ Please explicitly solve this question by using Lagrange multiplier method. I accept $(x-2)^2+(y-3)^2=4$ ...
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### Set all measurable real functions on $[0,1]$ with metric $\int_{0}^1 \min \{1,|f(t)−g(t)|\}dt$ is Fréchet without nonzero continuous linear functional

Bounty Edit: In the following, all the questions will be highlighted by a bold number and a text written in italics. I found the following statement in a book, and I am really struggling to see why ...
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### Maximization problem on an ellipsoid [closed]

for three variables, $$\max f(x,y,z)= xyz \\ \text{s.t.} \ \ (\frac{x}{a})^2+(\frac{y}{b})^2+(\frac{z}{c})^2=1$$ where $a,b,c$ are constant how to solve the maximization optimization problem? ...
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### How to write a discrete dynamical system into first order system

I need guidance on how to solve this here. $$x_{n+1} + 3x_n - 4x_{n-1} = (\sqrt{2})^n cos \left(\frac{n\pi}{6}\right)$$ I am required to transform the above equation into a first order finite ...
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### Marginalizing multivariate-normal distribution canonical form

Regarding the problem of margenalization of canonical forms of multivariate gaussian distribution it was mentioned in probabilistic graphical models text book that $$\int{C(X,Y;k,h,g)}dY$$ is ...
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### Expectation Functional in Lebesgue and Riemann Terms – Looking for a clarification

Here there is a really central problem I am having self-studying probability theory, that concerns the relation between the definition of expectation in Lebesgue terms and in Riemann terms. I will ...
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### Negative Mean Square Error

For simple random sampling, I have calculated somemean square errors for ratio-type estimators such as Isaki estimator, and Prasad Singh estimator. But, Mean Square Errors i obtained are negative. ...
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### Is It Worth It Working Out Every Practice Problem In Math? (Without a calculator)

I'm bouncing back between trig, algebra, and calc books. I've noticed that most of the problems at some point seem to distill into very tedious arithmetic. It is nice to have the prowess of ...
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### Suitable reference for learning symplectic geometry

I am interested in studying symplectic geometry by myself and I'm looking for a good text to use as a reference in the way. I am a bit lost because I've found a lot of notes and books on the subject ...
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### Does the phrase “If you don't use it, you lose it” apply to mathematics? [closed]

I'm asking this because I ran into the following particular situation: I took some calc courses over 2013, where I learned, amongst other things, to integrate some pretty nasty functions, and this ...
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### writing a piecewise regression model as a linear model

lets write the following piecewise regression model $$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0$$ $$y=\beta_0 +\beta_1 x + \epsilon \ \ x\gt x_0$$ according to the variable $x_0$ is known,...
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### Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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### Between Oksendal and Karatzas books

I finished Oksendal "SDE , an introduction with applications" , did most of the exercises (not all with success, but I read the solutions for those); my next project would be to read the Karatzas "...
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### proving if $a \le b$ then $\sup(A) \le \inf(B)$

Let $A$ and $B$ be bounded sets of real numbers such that $a\le b$ for all $a \in A$ and for all $b \in B$. Show that $\sup(A) \le \inf(B)$ Pf: Assume A and B are bounded sets. This means they have a ...