Questions tagged [solution-verification]
For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" or "where is the mistake?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplication.
46,150 questions
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Limiting Distribution of the MLE for a restricted Normal distribution
Problem: Let $X_1, \dots, X_n$ be iid drawn from the family of $N(\mu, \sigma^2)$ where we restrict $\mu \geq 0$. We'd like to find the limiting distribution of the mle of $\mu$.
It can be shown, and ...
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Find a function $f$ which is continuous on $[0, 1]$ and satisfies given conditions
Q) Suppose $0 < a < 1,$ but that $a$ is not equal to $1/n$ for any natural number n. Find a function $f$ which is continuous on $[0, 1]$ and which satisfies $f(0) = f(1),$ but which does not ...
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How should I find its canonical form using the given transformations?
Homework problem: Classify the following partial differential equation $u_{xx}+6u_{xy}-16u_{yy}=0$ and find its canonical form using the transformations $\xi=-8x+y, \eta=2x+y$.
Here's my work:
...
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Proof of Chasles theorem (Kinematics)
I have been trying to prove Chasles theorem using linear algebra. I am especially doubtful about whether the matrix can be inverted in the plane $\Pi$. And does this theorem also hold for ...
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Solving mathematics problem, check my answer.
A project can be done by $20$ employees in $30$ days. But, in $11$-th and
$12$-th days, the project is stopped. The project continued at $13$-th
days. In $24$-th days, only $16$ employees work until ...
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Continuity of the homotopy between [f*f']and f(0) shown by Hatcher for the fundamental groupoid [closed]
In the book Algebraic Topology by Allen Hatcher, he defines the fundamental group but seems to have omitted the proof that the homotopy defined between $f_{t}*\bar{f_{t}}$ and the constant path at $f(...
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Show that $\inf_{x\in \mathbb{S}^{n-1}}\|Ax\|_2\le s$ if and only if there exists $x\in \mathbb{S}^{n-1}$ such that $ \|Ax\|_2\le s$. [closed]
Fix a matrix $A\in \mathbb{R}^{n\times n}$. I try to show that the following two sets are the same:
$$
\inf_{x\in \mathbb{S}^{n-1}}\|Ax\|_2\le s\Longleftrightarrow\exists x\in \mathbb{S}^{n-1}: \|Ax\|...
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solution-verification | Prove that the complex number $ (a_1 a_2 + i)(a_2 a_3 + i)\cdots(a_n a_{n+1} + i) $ has positive real and imaginary parts.
The problem
Let $ n \geq 2 $ and $ a_1, a_2, \dots, a_n $ be distinct positive integers.
Prove that the complex number
$$
(a_1 a_2 + i)(a_2 a_3 + i)\cdots(a_n a_{n+1} + i)
$$ has positive real and ...
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solution-verification | Determine which nonempty subsets of $\{1, 2, . . . , n\}$ are more, those with odd sums or those with even sums.
the problem
Let $n \geq 3$. Determine which nonempty subsets of
$\{1, 2,..., n\}$ are more, those with odd sums or those with even sums.
my solution
So I took 2 cases:
If n is even, then in the set ...
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Checking: Have I found all solutions to this functional equation?
I encountered the following problem online:
Given that $f(x+2) + f(x^2) = x^2+x+14$,
what is $f(x)$?
Hint: $f(x)$ is linear.
I was able to solve it as follows:
First I substituted $x=-1$ into the ...
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How do I apply the Chain Rule in this example?
I have the following question:
I know that given functions $x(t),y(t),z(t)$ and $f(x,y,z)$, then
$\frac{df}{dt}=\frac{df}{dx} \frac{dx}{dt}+ \frac{df}{dy} \frac{dy}{dt}+\frac{df}{dz} \frac{dz}{dt}$.
...
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Is this proof that $\sum_{n=0}^\infty\frac{\sin2nx}{(2+\sin x)^{n^2}}$ does not converge uniformly on intervals containing $-\frac{\pi}{2}$ correct?
I have provided an answer to this question prooving that $\displaystyle f(x)=\sum_{n=0}^\infty\frac{\sin2nx}{(2+\sin x)^{n^2}}$ does not converge uniformly on any interval containing $\displaystyle-\...
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Simpler Proof of Permutation [closed]
A very very informal proof that I just wrote, that I thought was more intuitive than other proofs I could find on here/on the internet.
n: number of choices r: number to choose out of chocies
nPr=n!/...
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Prove that dim null 𝑆𝑇 ≤ dim null 𝑆 + dim null 𝑇.
So, I've been working through Linear Algebra Done Right, and I was unsure about my solution for one of the problems; here it is:
Suppose $𝑈$ and $𝑉$ are finite-dimensional vector spaces and $𝑆 \in \...
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Show that $\prod_{v\in S} K_v^{*} \to C_K$ is not a closed embedding.
I want to prove this:
$K$ is a number field. If $S \subset V_K$ is a finite set of places and $|S| > 1$, then $f:\prod_{v\in S} K_v^{*} \to C_K$ is not a closed embedding. ($C_K=\mathbb I_K/K^*$ is ...
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