# All Questions

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### how can I Find a 95% credible interval for p using the Bayesian method with the uniform distribution as a prior for p?

When I have a RV X~Geom(p): $x\ Frequency\\ 1 7459\\2 1930\\ 3\ 463\\ 4\ 117\\ 5\ 22\\ 6\ 6\\ 7\ 2\\ 9\ 1$ This is what I am trying to do: Since p is a probability, I say that $p\sim U[0,1]$ An ...
29 views

### The coefficient of $t^n$ in $\left(\sum_{k=1}^{n-1} t^k\right)^r$

I'm trying to count the number of ways of writing a general natural number $n\geq 2$ as the sum of $r$ smaller numbers where each of these numbers is at least $2$ - that is, I want to count the number ...
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### $G$ is a finite solvable group ,then there exist prime $p$ if $H$ is a Hall subgroup of $G$ that $p \nmid|H|$ then we have $H \lneqq N_{G}(H)$.

suppose $G$ is a finite nontrivial solvable group ,then there exist prime $p$ which if $H$ is a Hall subgroup of $G$ that $p \nmid|H|$ then we have $H \lneqq N_{G}(H)$. my work:we know that $G$ has a ...
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### Show that days with the identical calendar date in the years 1999 and 1915 fell on the same day of the week.

I think I'll be able to work this problem if I understand the quesiton. I am having difficulty in interpreting the problem(the phrase "identical calendar date" is throwing me off). Any help is ...
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### implications of unimodality of distribution

Suppose $X$ is a continuous r.v. such that $X\ge0$ and its distribution is unimodal. What sort of consequences does that entail for $X$ in terms of its other properties (e.g., moments, etc.)?
20 views

### Deriving the normal distance from the origin to the decision surface

While studying discriminant functions for linear classification, I encountered the following: .. if $\textbf{x}$ is a point on the decision surface, then $y(\textbf{x}) = 0$, and so the ...
28 views

### A generalization of the Sokhotski–Plemelj theorem

The Sokhotski–Plemelj theorem on the real axis states: $$\lim_{\varepsilon\rightarrow 0^+} \int_a^b \frac{f(x)}{x\pm i \varepsilon}\,dx = \mp i \pi f(0) + \mathcal{P}\int_a^b \frac{f(x)}{x}\, dx$$ ...
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### Convergence in law of random variables

Let $X_1,\ldots,X_n \overset{i.i.d}{\sim} \ Uniform(0,1)$ and write $M_n = \max(X_1,\ldots,X_n)$. If we have proved that $M_n \overset{a.s.}{\rightarrow} 1$, then we know that $(M_n)$ converges in ...
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### Solving a combinatorial problem using inclusion-exclusion

we have to make n with k integers.k integers will have to be choosen from k ranges.Every range has a minimum value and a maximum value.In how many ways we can make n according to the conditions.For ...
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### self orthogonal binary code

I know the definition of a self-orthogonal (or weakly self-dual) code; however, I am experiencing a bit of a trouble in building such codes - well, except trivial ones, but that is not interesting. ...
31 views

### Sigma Notation for Power

How do I evaluate the telescopic sum for these two? (You do not have to provide the answer if you feel like you dont want to) I never worked with sigma notation regarding powers. Question 1 ...
21 views

### Dirac delta composed with a function and implicit equation for the roots

I'm considering an expression of the form $$\int_{-\infty}^\infty dx G(x) \delta(x^2-f(x)^2)$$ where $G$ and $f$ are two unrelated smooth functions of $x$. Now I know that when $f$ is a positive ...
31 views

### Algorithm Generate all labeled graphs

I'm trying to find an algorithm which will generate all labeled graphs with $n$ nodes and $n-1$ edges. It must cover trees and graphs with cycles with one unconnected node, but without multigraphs. ...
25 views

### Queue-length and waiting time of M/D/1-queue

I studied the M/G/1 queue by myself. Now as an application, I considered the M/D/1- queue. I know that the results can be find in the internet, but I haven't seen any calculations. Let $Q$ be an ...
23 views

### How to generate random symmetric unitary matrices “close” to a given matrix?

Note: This question have been asked in Mathematics Stackexchange [click here]. Since random matrix has close relation with some physical problems, I would like to post it here again. Sorry if this ...
23 views

### Lower bound on numbers in “extension” to Lagrange four square theorem

Can we find a representation of positive integers $n$ as the sum of six (or more, if you wish) squares in such a way that there is a (non-trivial) lower bound for the smallest square, in terms of $n$? ...
9 views

### Prove the A x B lexicographical ordering is partially ordered

Is this proof? I think I may have the right ideas, but I'm not sure.
11 views

### Finding the best transformation for a triangle (Jacobian)

A triangle in xy-plane has following vertices: (0,0) (2,3) (3,0) Book gave the following transformation in uv-plane and it works out nicely, but I am not sure ...
6 views

### Entire function and biorthogonal set.

Let us suppose that $\{e^{i\alpha_n x}\}$ has a biorthogonal set and let us consider $$H(w)=\int_{-\pi}^{\pi}h_0(x) e^{iw x} dx, \ \ \ \ w\in\mathbb C$$ such that $H(\alpha_n)=0$, $n\neq 0$ where ...
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### Product of self adjoint transformations

If $A$ and $B$ are linear transformations such that $A$ and $AB$ are self-adjoint and such that $\ker (A) \subset \ker (B)$, then does there always exist a self-adjoint transformation $C$ such that ...
24 views

### Define another Equivalence Relation from Geometric Figure?

Define relation $W$ on $R^2$ by $(x_1,y_1)W(x_2,y_2)$ whenever $x_1−y_1=x_2−y_2$. I have the equivalence classes to be given by $f^{-1}(r)=\{(x,y)\mid x−y=r\}$, where $r∈R$. So how would you define ...
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### proof of separability hilbert space H.

I think that a Hilbert space is called separable if it contains a complete orthonormal sequence. Finite dimensional Hilbert spaces are considered separable. I need to prove that the Hilbert space ...
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### Continuous wavelet over piecewise functions

Is there a wavelet function that spans the space of piecewise: linear functions(as Haar is a basis for piecewise constant functions) polynomial functions I am almost sure there is one for ...
26 views

### removable singularity and injective function

Let $U \subset \mathbb{C}$ a conected open subset, $a \in U$ and $f:U- \{a\} \to \mathbb{C}$ a holomorphic function such that $V=f (U-\{a\})$ is a open bounded subset. (A) Show that $f$ has a ...
27 views

### Fourier Series Transform of Full-Wave Rectifier

A first step in converting AC-power from the power-grid to the DC-power that most devices need is to utilize a full-wave rectifier. A full-wave rectifier converts a sinusoidal input (Asin(omegaot) ...
29 views

### Modular Equation and Modular Forms?

I'm reading Ramanujan's Notebook now and I see some kinds of "Modular Equation". At first I think Modular Equation is just a set of interesting fomulaes, but wikipedia says that Modular Equation is ...
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### What's the rank of a matrix that has constant number ones in each col/row over $F_2$

Let $A$ denote a $n\times n$ matrix over $F_2$, which means $A \in \{0,1\}^{n\times n}$. Also assume that each row and each column only has exactly 3 ones. 1) What is the upper bound and lower bound ...
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### Form Poset from (Non-zeta) Matrix

I have a matrix (well, really a table) of values that are the results of various indicator systems. Naturally, each system is slightly discordant, so no one true ranking exists. I'm looking to form ...
21 views

### Properties of Functions 2

For each part of this problem, give sets A,B, and C, with C ⊂ A, and a function f : A → B satisfying the given conditions. Or, if no such function exists, prove that none exists. (There is no need to ...
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### What is the Vapnik-Chervonenkis dimension of sigmoidal functions?

Consider the following class of functions: $F=\{f_w:R^d \rightarrow [a,b], f_w(x)=\sigma(w^Tx), \forall x\in R^d\}$, where $\sigma(\cdot)$ is a sigmoidal function (e.g. tanh, or sigmoid so it has ...
27 views

### What is a Serre presentation of a Lie algebra?

For example, as in: Give a Serre presentation of Lie algebra $\frak{g}$ of type $G_{2}$. Is it the presentation in terms of Chevalley generators, which satisfy Serre relations?
36 views

### Optimization for minimizing average cost

I was given the function of $C=Tq^{\frac{1}{a}} + F$ where $C$ is total cost, $q$ is output, $a$ is a positive parametric constant, $F$ is the fixed cost, and $T$ measures the technology available ...
29 views

### Help needed on Green's theorem.

Using Green's Theorem, find the area of the region formed by the intersection of $$x^2 + y^2 \leq2 \text{ and } y\geq1$$.
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### Proof that no Eulerian Tour exists for graph with even number of vertices and odd number of edges

How would you prove that for a connected graph with an even number of vertices and an odd number of edges, at least one of the vertices has an odd degree? My first attempt at solving this has been to ...
24 views

### Deriving single linear regression parameters in terms of multiple linear regression parameters

Suppose the true population model is ln(wage) = B0 + B1(education) + B2(experience) + v (v is error term) Suppose the model is estimated as ln(wage) = B3 + B4(education) + u How do I calculate ...
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### representing intervals as infinite intersectiom or union

I searched for this questions but didn't fine the topic yet. I'm just curious if there is an "easy" way of representing intervals in $\mathbb {R}$ as infinite intersection and or union. For example, ...
What is the difference between thin triangles and slim triangles in $\delta$ hyperbolic spaces? Google search seems to consider thin and slim as synonyms and shows the same results for the two.
So I just proved that if $f$ is analytic on $\overline{\mathbb D}$, and $f(\partial\mathbb D) \subset \partial \mathbb D$, then it extends to a rational function on $\mathbb C$. What if we weaken this ...