0
votes
0answers
13 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
22 views

$G$ 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 ...
0
votes
0answers
19 views

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 ...
0
votes
0answers
14 views

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.)?
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votes
0answers
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 ...
0
votes
0answers
28 views

A generalization of the Sokhotski–Plemelj theorem

The Sokhotski–Plemelj theorem on the real axis states: $$ \lim_{\varepsilon\rightarrow 0^+} \int_a^b \frac{f(x)}{x\pm i \varepsilon}\,dx = \mp i \pi f(0) + \mathcal{P}\int_a^b \frac{f(x)}{x}\, dx $$ ...
0
votes
0answers
24 views

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 ...
0
votes
0answers
21 views

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 ...
0
votes
0answers
16 views

Standard examples of operator

In a text I am reading it says that we can consider an operator $A: X \rightarrow X^{*}$ (where $X := W^{1,p}(\Omega)$) which is defined as $$Au = -\text{div}(a(x,u,\nabla u))$$ where $a: \Omega ...
0
votes
0answers
25 views

Maple - Error, `-` unexpected

I'm working with a 3 by 1 matrix in maple whose members are very very large expressions including sines and cosines. I have derived the matrix in Maple before and then pasted in MS Word. After some ...
0
votes
0answers
18 views

Compute the inverse fourier transform of $ e^{-Af} $ and $ e^{-A\sqrt{f}} $

I want to compute the inverse fourier transform of $ e^{-Af} $ and $ e^{-A\sqrt{f}} $, where $A$ is a constant and $f$ is frequency. In the case of $ e^{-Af} $, I tried to solve it from the Fourier ...
0
votes
0answers
17 views

Basic questions about Counting Process

I am learning Counting Process in my probability course. The following comes from Sheldon M. Ross*'s *Introduction to Probability Models: If we say that an event occurs whenever a child is born, ...
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votes
0answers
27 views

Degenerate eigenvalue and minimal polynomial

I'm learning about elementary linear algebra and I am confused on a specific point related to minimal polynomial. When we have non degenerate eigenvalues it is just equal to the characteristic ...
0
votes
0answers
10 views

Showing that the operations defined on a right ring of fractions are well-defined

My problem comes from Goodearl & Warfield's "An Introduction to Noncommutative Noetherian Rings". Let X be a right Ore set of regular elements in a ring R. Define a relation $\sim$ on $R ...
0
votes
0answers
28 views

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. ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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. ...
0
votes
0answers
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 ...
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votes
0answers
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 ...
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votes
0answers
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 $n$? ...
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votes
0answers
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.
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
14 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
9 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
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) ...
0
votes
0answers
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 ...
0
votes
0answers
17 views

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 ...
0
votes
0answers
50 views

Total curvature of a piecewise smooth planar curve

I am trying to show that the total curvature of a piecewise smooth planar curve $\alpha$ has the property that $\displaystyle \int_{C}\kappa $ $\text{d}s + \displaystyle \sum_{j=1}^{l} \epsilon_{j} ...
0
votes
0answers
40 views

Calculate 1D random walk with alternating step size expected iterations to return to origin

I'm trying to solve a problem as outlined below; I'm a bit new, however, and I'm not sure how I could solve this problem. Assume someone has lost their keys, and uses an inefficient random walk to ...
0
votes
0answers
20 views

The Area of Right Triangle and Integral

Consider that we are dealing with a right triangle with constant base ($B=B_1$ and $\frac{dB}{dt}=0$). The values (of $B=B_1$ and of $\frac{dB}{dt}=0$) are maintained by nature to be constant from ...
0
votes
0answers
23 views

Intertialess Gear Train transducer differential equation setup

The system below shows two rotational inertias, I1and I2, connected by a gear train. An ideal gear train is inertialess. Notice that there are no rotational springs and dampers, just the two inertias ...
0
votes
0answers
23 views

Logic negate and simplify

Negate and Simplify: [(pvq)->~r]v~q Can someone show me step by step how to go about this. I am a little confused about negating over an implication.
0
votes
0answers
27 views

Function Proofs

Suppose that $f : A → B$ is a function. If $S ⊆ A$, then we define $f(S)$ to be the set $f(S)={f(x) : x∈S}$. (So for example, if $f : R → R$ is given by $f(x) = x^2$, then we have $f({1,2,3}) = ...
0
votes
0answers
7 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
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?
0
votes
0answers
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 ...
0
votes
0answers
29 views

Help needed on Green's theorem.

Using Green's Theorem, find the area of the region formed by the intersection of $$x^2 + y^2 \leq2 \text{ and } y\geq1$$.
0
votes
0answers
32 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
20 views

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, ...
0
votes
0answers
9 views

Thin triangles vs Slim triangles in hyperbolic spaces

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.
0
votes
0answers
22 views

Analytic continuation past the disk

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 ...

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