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how would I find the mgf of a gamma rv with parameter k > 0 and λ > 0 ?
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How can you show a function is a cumulative distribution function and then how can you show this cdf describes a continuous random variable?
The problem reads:
Let $\{ E_j : j\in J \}$ be a collection of connected subsets of a metric space $X$ such that $E_i \cap E_j \neq \emptyset$ for every $i,j\in J$. Prove that $\cup _{j\in J} E_j$ is connected.
Before marking this a duplicate, please consider that I am aware that there are...
I am Currently studying for my preliminary exams (Advanced Calculus and Linear Algebra), and I can solve about half of the previous years exam questions. However, I do not have anyone to vet my proofs at the moment. My question is it appropriate to ask a large number of questions on here?
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Q: Problem 12.22 on Analytic Semigroups In Renardy's An Introduction to Partial Differential Equations
I saw that this question was protected and the accepted answer referred to another older post which wasn't.
At a minimum, shouldn't the older one be protected as well?
Also, shouldn't the newer one be possibly marked as a duplicate? While they differ at a first glance, they are really talking ...0
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I have trouble solving this task:
Let $Y_1 < Y_2 < Y_3$ denote the order statistics of a random sample of size
3 from a distribution with pdf $f(x) = 1$, $0 < x < 1$, zero elsewhere. Let $$Z =
\frac{(Y_1 + Y_3)}{2}$$ be the midrange of the sample. Find the pdf of $Z$.
So far I have got this:
...
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How do you find the change of basis matrix from a Basis to a standard basis for a 2x2 matrix A?
Trying to get Necromancer badge i answered this question. Why i have not badge? This question is asked in 2009 year. Maybe Answer means answer marked as answer?
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I have following three equations $$ u'' - 2u = -2v$$ $$ u(0)=0 $$ $$ u'(1)=0 $$
and from these 3 equations I am trying to find u(v).
It looks to me "Cauchy-Euler Differential Equations - Nonhomogeneous case" but I am not sure about that because it is not an exactly Cauchy form. Could you help m...0
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Why is $B_n = \{f \in L_1 : \int |f|^2 < n \}$ a nowhere dense subset of $L_1$? Please provide a proof without assuming that $L_2$ is a proper subset of $L_1$.
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let be $Z$ random variable, $Y_i$ iid random variable, $E(Y_i)=\mu$ , $var(Y_i)=\sigma^2$; $Z$ and $Y_i$ are independent.
show that $E(X^2|Z)=\mu^2Z^2+\sigma^2Z$.
I compute $E(X^2|Z=n)=nE(Y^2)+n\mu^2$ and i remplace the quantity $E(Y_i^2)$ by $var(Y)+(E(Y))^2=\sigma^2+\mu^2$, but i dont get th...0
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1)the team has six boys and five girls?
2)there are at least one boy and at least one girl on the team?
In how many ways, can one select n letters from an unlimited supply of A’s, B’s and C’s so that there
is an even number of A’s?
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$$\int^{2}_{0}\int^{0}_{-\sqrt{1-(y-1)^2}}xy^2dxdy = -0.8$$
I have evaluate this by changing to polar coordinates.
I have sketched it and decided that
$$\int^{0}_{-1}\int^{3\pi/2}_{\pi/2}r^4 \cos\theta \sin^2\theta d\theta dr = -2/15$$
but as you can see my answer differs from what is needed....
What is the definition of killing field?. The one my professor told me is : a smooth vector field V on M is called a Killing vector field for g if the flow of V acts by isometries of g.
So what does it mean by the flow of V acts by isometries?
I suspect this definition is equivalent to saying ...
There is a considerable amount of questions of the type
Can you see if my proof/solution is correct?
My question is simple: are they on-topic?
My point is two-fold: I think they fail usefulness (and even create confusion) and may not be on-topic.
With regards to the first aspect, sometime...0
Let there be a triangle with angle $A,B,C$
Prove that the distance from circumcentre and orthocentre is $whole square root of (1-8cosAcosBcosC)
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How can one solve the following differential equation by the technique of separation of variables?
$$\frac{1}{x^2}\frac{dy}{dx}=y^5 \text{, when, }y(0)=-1$$
How do I determine whether this function is continuous at x = 0?
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Let $$f(z)=\dfrac{z-a}{z-b},\,\,\,\,\,\,z\not=b$$ be a complex valued rational function.
How can I show that,
if $|a|,|b|\lt1,$ then there is a complex number $z_0$ satisfying $|z_0|=1$ and $f(z_0)\in\mathbb{R}$ ?
I have tried in many ways, but on success. Basically I tried to show that there...0
This triangle is not parallel or vertical, it's in a 2d plane.
Problem Triangle, missing point
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I cannot for the life of me see why my solution method gives me the wrong result.
A machine works for an exponentially distributed time with rate $\mu$ then fails. A crew checks the machine at times according to a Poisson process with rate $\lambda$; if the machine has failed, it's immediatel...
A point $(a,b) \in [0,1]^2$ is selected at random. Let $X: [0,1]^2 \to [0,2]$ be the random variable that maps every point to the sum of its components, i.e. $X(a,b) = a + b$. Find the CDF $F(x) = \mathbb{P}(a + b \leq x)$ by considering the cases $0 \leq x \leq 1$, $1 < x \leq 2$ and $2 < x$ ...
Prove that every set of $2k$ integers has elements of opposite parity differing by at least $2k-1$ or elements of equal parity differing by at least $4k-2$
I'm pretty new to AskUbuntu's review section. IMHO, I review by doing some search before taking any decisions. But, hey! that is me.
My question is, do we allow editing averagely voted answers with adding few more information? e.g.:
What is the linux-image-extra package for and do I need it?
...0
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Show that $x^4+1$ is irreducible over $Z_p$ for every prime $p$.i have done it for $p=2,3$.but no idea as to how to do for general $p$??
Today i come across something very odd a browsing throw site i saw a specific question page asked me for username and password!!
what is it?
is this a bug?
please take a look your self, it happens with every browser and not dependent to if you are logged in or not.
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If $f(x)\geq 0$, is continuous in the interval $[0,\infty)$ , and $\lim_{x\to \infty} f(x)=0$, then $\int_1^{\infty} f(x)dx$ is finite.
This is true or false.
Please someone help me.
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How to prove that
$$(\frac{1+\tanh x}{1-\tanh x})^3=\cosh 6x+\sinh 6x$$
I have tried using the Dmoivres theorme
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So for my particular power series, I find that my interval of convergence is
-3 \lt x \lt 3
so R \eq 3
I do a nth term test on the original equation with -3 and 3 and find that the series converges on these values. Does that mean the series is absolutely convergent at -3 \lt x \lt 3 and condi...
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Let $(x_\varepsilon,y_\varepsilon)\in[0,1]\times[0,x_\varepsilon)$ be a sequence such that $(x_\varepsilon,y_\varepsilon)\to(x,y)\in[0,1]\times[0,x)$ as $\varepsilon\to0$.
Is there an integrable function $f:[0,1]\to\overline{\mathbb{R}}$ such that
$$
-\inf_{\varepsilon>0}\frac{\chi_{[0,y_\v...-1
Today, I was exploring the featured section of SO and I happened upon this question:
Demystifying sharedctypes performance
They question itself was fascinating, but look at the answer! Its like a mile long! I read it all and I think I learned a thousand things just reading it. It was amazingly ...
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Provide a complete proof or counterexample for each property. And I have no idea what I'm doing.
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I tried to answer the following exercise:
Let $S$ be a nonempty set with an associative operation that is left and right cancellative. Assume that for every $a$ in $S$ the set $\{a^n \mid n=1,2,3, \dots \} $ is finite. Must $S$ be a group?
My thoughts:
Take the group $G = \mathbb Z / 5 \mathbb...
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I am trying to prove $\mathbb{Z}^{\oplus \mathbb{N}} \times \mathbb{Z}^{\oplus \mathbb{N}} \cong \mathbb{Z}^{\oplus \mathbb{N}}$ and will appreciate hints to approach the question.
Background:
This question is taken from Aluffi.
$\mathbb{Z}^{\oplus \mathbb{N}}$ is defined as $\{ \alpha \col...0
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I came across this question in the review queue.
The user gives a vaque answer (I am not really familiar with this topic) and afterwards promotes a playlist in his YoutubeChannel.
The playlist is about Hadoop as also is the question.
It also is rather lengthy and seems to be of ok-quality.
Is ...0
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Let $a,b$ be two group elements of finite order that commute.
I thought that $|ab| = \text{lcm}(|a|,|b|)$. My proof was that $(ab)^n = a^n b^n =e$ if and only if $a^n = b^n = e$ if and only if $|a|,|b|$ both divide $n$. The smallest $n$ such that both orders divide it is the least common multip...
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Is a real analytic function equal to its Taylor series at the endpoints of the interval of convergence, provided the series converges a the endpoint?
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I just stumbled over the following question:
Tag synonyms: android-avd and avd
Question:
I would be interested in: what should be preferably used in general and are there some rules regarding tag creation and usage?
If there is a risk of confusion, wouldn't it be better to generally use
androi...0
I have the function $f(x) = e^{-\frac{1}{x}}e^{-\frac{1}{1-x}}$, which produces this graphic.
What should $f(x,y)$ be to look like a 'hill', i.e. $f(x)$ spinned about vertical axis?
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Yesterday I sat for my Real analysis II paper. There I found a question asking to integrate $\int_{0}^{1}xe^x$ without using antiderivatives and integrating by parts.
I tried it by choosing a partition $P_n=(0,\frac{1}{n},\frac{2}{n},.......\frac{n-1}{n},1)$. But I was not able to show that $li...
I would like to write a notation for a linearly spaced vector. This vector has 21-scaler or element. The max of vector is starting point and min of vector is stopping point. Min is max times 0.2, and the rest of elements were linearly spaced between max and min. May someone help me to write t...0
First off, this is not the classic case of "My name is not showing as editor" as cited here and here. Two of my recent edits were recently taken over by users with 2k+ reputation. First one was this. When I proposed the edit, the user had everything jumbled up in code block. I rectified it. Later...
The Legendre Polynomials are defined by $L_n(x) = \frac{d^n}{dx^{n}} (x^2 - 1)^n$. The inner product in this case is defined on $[-1, 1]$ as follows:
$<f(x), g(x)> = \int_{-1}^{1} f(x)g(x)dx$.
I'll denote the arbitrary polynomial of degree n by $P_n(x)$. Since it is orthogonal to $\{1, x, ..., ...
Question is in the title. Can't find the info any where. Thanks.
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$$Log(-e i)$$
My try:
$$=\ln|0+(-e)i|+i[\arg (0+(-e i))+2\pi k]$$
$$=\ln|e i|+i(-\frac{\pi}{2}+2\pi k)$$
My attempt is correct?
As the title says, nothing about the dimensions of the matrix is mentioned? What should I be starting with here? I just know $$|A-\lambda I| = 0 \\ and \\ A^3=I$$
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The question states... Let phi: G to G be a homomorphism with the map phi(g)=g^2. Prove phi is abelian.
So far I have:
Let g and h be in G. Then phi(g)=g^2 and phi(h)=h^2. Since we know it is a homomorphism,
Phi(gh)=phi(g)*phi(h)=g^2*h^2....
But I don't know how to make a connection that they...
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I feel confuse with the next permutation. We have 4 step for find the next permutation.
step 1: find from right to left and check a[i] < a[i+1].
step 2: find the pivot with condition is a[k] < a[i].
step 3: swap a[i] vs a[k].
step 4: sort list with reverse.
how to generate the next permutation o...
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The question asks to find an example of a homomorphism of D4 to Z8 such that ker={e,R,F}.
D4 = {e, R,R^2,R^3,F,FR,FR^2,FR^3} and Z8={0,...,7}
I thought about letting the map equal:
Phi(e)=0
Phi(F)=0
Phi(R)=0
But I wouldn't know how to map the other elements...
Phi(R^2)=
Etc
Say I have sampled some points in $[0,1]^2$ and evaluate a function $f(x,y)$ for them. I am interested in the behavior of $f$ along a single dimension.
If the points were like $(x_1,y_1),(x_1,y_2),\ldots,(x_1,y_N)$, then they lie nicely on a straight line, such that I can compare $f(x_1,y_1),f(...0
$$x \propto y^2$$
How is it different from saying:
$$x \propto y$$
That is; when we say that Two variables are proportional then it means that two variables are related such that when one is zero other is too. And change in one variable is accompanied by change in other. This is a general defi...
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I have no idea to start or consider the integral
\int_{0}^{\infty} e^{-e^{x}}dx
any hint or solution would be highlt appreciated.
Thank you.
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I'm trying to solve a problem set for my functional analysis course and I'm stuck at the following problem:
Decide if the following problem has a minimizer
Let $g\in C^0([0,1])$. Minimize $\|f-g\|_{L^\infty([0,1])}$ among all $f\in L^\infty([0,1])$ with $$\int_0^1\,f\,dx=0$$
Hint: C...
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I know that there does not exist a onto homomorphism from $Z_8$ ⊕ $Z_4$ to $Z_4$ ⊕ $Z_4$ but what about into homomorphisms. How many of them exist and how to find them.
Also, How many 6-digit phone numbers have distinct digits, and don’t start with 0.
When you edit a post with the edit button, the post is edited and the post signature is directly updated with the editor's signature:
However, when using the inline tag edit feature (10k+ user feature):
the post is edited but the post signature is only updated after a page reload.
I believ...0
I have some troubles with variational formulations of pdes.
I'm considering $\chi\in H^1(\Omega)$ is the solution to the elliptic mixed boundary value problem
$$
\begin{cases}
\nabla\cdot(\mu \nabla\chi)=\nabla\cdot(\mu\chi)\;\,\text{in}\,\Omega\\
\mu\nabla\chi\cdot n=\mu v\cdot n\;\,\text{on}\,\...
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Q: Find the value of $f'(2)$ where $f(x)=\lim_{n\to\infty}\sum_{n=1}^{n}\arctan(\frac{x}{n(n+1)+x^2})$
Find the value of $f'(2)$ where $f(x)=\lim_{n\to\infty}\sum_{n=1}^{n}\arctan(\frac{x}{n(n+1)+x^2})$
I could not find $f(x)$ here.I had a feeling that Riemann integral should be used to find the $f(x)$ but i cannot find after some efforts.Please help me.
Definition of eccentricity:
Let $N$ be a surface. Consider $[R(N), r(N)]$ to be the smallest interval such that $N$ is contained in the annulus $D_R \setminus D_r$. We define the eccentricity as
$\Theta(N) =R(N)/r(N)$.
Now, I consider level-sets of a function $v$ in $\mathbb{R}^n \setminus \{...
I have suggested some edits and 5 of them were approved. But reputation didn't added up. Same for yesterday. Is something wrong?
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I am beginner in probability theory. In order to make a better understanding of Borel Sets, Measurable Space and Random Variable, I need to learn about algebra and sigma algebra, Can anyone please suggest any good book that covers these topics for beginners with sufficient questions (questions on...
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I have an objective function which is given as:
$f=x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8$
S.T.
$x_1+x_3+x_5+x_7=2$
$x_2+x_4+x_6+x_8=2$
$x_1(x_2)=0$
$x_3(x_2+x_4)=0$
$x_5(x_2+x_4+x_6)=0$
$x_7(x_2+x_4+x_6+x_8)=0$
Given the above constraints I want to know if and how this problem can be solved u...
Please find the exact value of an infinite series $\sum r^{n(n+1)}$ for $0<r<1$ .
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Q: let v amd w be the subspaces of R^2 spanned by (1,1) and (2,2) find victors v amd w so v+w=(2,-1)
I don't get it, a guy was pointing out some problem in Spring, I've filled a ticket for the exact same problem and got it accepted.
So why was my answer linking to the ticket deleted/converted to a comment? I got
This does not provide an answer to the question. To critique or
request clar...
I don't understand that vertical bar?
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Let $(X, \mathscr{A}, \mu)$ be a finite measure space. Let $f_n \in L^1$. Assume $f_n \rightarrow f$ a.e. and there exist $p > 1$ and $c > 0$ such that $$||f_n||_p < c$$ for all $n$.
I want to show that $$f_n \rightarrow f \ \mbox{in} \ L^1, \ \mbox{i.e.,}\ \int_X |f_n - f| d\mu.$$
Since $f_n \...
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I was reading a paper and I found stated without proof or reference the following inequality:
$$\left(\sum_{i=1}^{m}\prod_{j=1}^{n}(\beta_{i}^j)^p\right)^{\frac{1}{p}}\leq \prod_{j=1}^{n}\left(\sum_{i=1}^{m}\left(\beta_{i}^{j}\right)^{p_j}\right)^{\frac{1}{p_j}}$$
where $\beta_i^j\geq 0$ and $\...
Let $f:\mathbb R\to\mathbb R$ a continuous function. Show that $f(U)$ is open when $U$ is open $\iff$ $f$ is a bijection.
Recently just got one chat room invite
http://chat.stackoverflow.com/transcript/96672
when i go inside nothing in. I don't know what's wrong. It's just show me room info and one message and also i can't send message in chat room.
what's wrong here?
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A circle has its center at (3,4). Find the slope of the tangent to the circle at (5,-2). The points can be drawn on the Cartesian plane.
How would you define Bayesian approach to probability in a concise down-to-earth way?
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Consider the following PDE.
$$
u_t=u_{xx}+f(u)-w,~~~~~w_t=\varepsilon(u-\gamma w),~~~~~~~(1)
$$
where $f(u)=u(u-a)(1-u), 0<a<\frac{1}{2}, \varepsilon,\gamma >0, \varepsilon\ll 1,\gamma\ll 1$.
A travelling wave for (1) is a solution that is a function of the single variable $\xi=x-ct$, i.e. $(u(\...
I often fall in such types of embarrassing situations. It thought to write it before, but did not write for my laziness.
However, all of you know that, a new user, with reputation point 1, can review suggested edits of his own question.
But most of these new users do not know that when a sugges...0
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The number PI has infinite decimals whom appear to be randomly distributed.
If we had PI fingers, and would therefore use PI as base instead of ten, could there exist other integers?
0
I just noticed that there is wlln. Could you guess what does it stand for..? It has only 11 questions and the topic is pretty broad. Its name is hard to search if you do not know that it exists, so it is probably useless. Maybe it should be renamed or merged with other tag that has more informati...
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I am stuck on the following question,
Find the matrix that represents the composite function GTS where
S(x,y,z) = (2x,y+z), T(x,y) = (2x + y, x + y, x-y), G(x,y,z) = (y,x,x,z)
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I have tried to simplify this expression for quite a long time now but I can't find how to do it.
Can someone help me with it.
Currently, you can see what teams a user belongs to, but IMO it would be a nice indicator to see the number of members (between brackets) in those teams.
Example:
Teams (3)
Stack Overflow (55) Stock Everflaw (13) Stork Babyboom (5K)
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Code fragments often appear in the title, and it is not pleasing to see it mixed within ordinary words, and it also takes a bit more time than regular words to recognize it.
I would like to have the title allow inline code formatting with backtick escapes, so that wherever the title appears on ...
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$$Res\left( \frac{e^z}{tan(z)}, \frac{\pi}{2} \right)$$ and $$Res\left( \frac{1}{Log^2(z)}, 1 \right)$$
Grateful if someone can show me a way to calculate these residues.
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Q: Infinite series $\frac1{1+\ln x}+\frac2{1+(\ln x)^2}+\frac4{1+(\ln x)^4}+\frac8{1+(\ln x)^8}+\cdots$
How do I prove that n!<(n/2)^n for n>=6, using mathematical induction?
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I've read this question on similar topic, but it's about closing a question by 5 people.
I do not know what to do when question is marked as a duplicate by a person with gold badge. I have a gold badge too and I do not agree, can I protest?
Five man can be enough for objective judgement but a si...
We have a population $p_j$ in year $j$ is governed by the following equation:
\begin{equation}
p_{j+1} = 2p_j + 3p_{j-1} + p_{j-2}
\end{equation}
I want to prove that the set of all sequences, p = $(p_0,p_1,p_2,...)$ for $j \geqslant 2$ is a vector space, denoted by V.
I started by taking 2 ve...
Google brought me to this question:
Is there a way to identify the busy (CPU-consuming) tab in Firefox?
But that question is marked as a duplicate of this one:
How to find out which firefox tab is using most CPU or memory?
The problem is that the second question already has an accepted answer...0
So I'm searching for an homomorphism of $A$-modules $f:M\mapsto N $ and some A-modules $M$, $N$ such both are finitely generated but Ker $f\subset M$ is not.
Thanks.
0
I am give the equation
Dew/dt = -1400(t-x)+350 where x
I have tried Dew/-1400 = t-x -.25
Dew/-1400 + x = (t-.25)dt
Dew -1400x = (t-.25)-1400dt
Not sure where to go from here and think it is wrong as well.
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I'm learning about complex analysis and need some help with this problem :
Let $\Omega$ open connected and $f : \Omega \rightarrow \mathbb{C}$ analytic such that $f(z) \neq z$ for all $z \in \Omega$. Suppose there exists $a \in \Omega$ such that $\left| f(a) - a \right| \leq \left| f(z) - z \...0
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Figure 1.4
I get stuck in here.
Should it be 10 11 100 101 110?
Thanks for your help!
0
Let $f(x)=\frac{q(x)}{p(x)}$ for some polynomials $q(x)$, $p(x)$ with $p(x)$ nonzero on $\mathbb{R}$. What are some necessary and sufficient conditions for "$f(x)=\frac{q(x)}{p(x)}$ being uniformly continuous on $\mathbb{R}$"?
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Does anyone has an idea how to prove that $$\sum\limits_{p = k}^{n - k + 1} C^{k - 1}_{p - 1} C^{k - 1}_{n - p} = \frac{n!}{(2 k - 1)! (n - 2 k + 1)!}?$$
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Q: How many orthogonal matrices(with a size of 3*3) are there, where all elements are whole numbers?
I need help in finding closed form for $$\Sigma_{i=0}^{log(n/2)} \frac{n}{2^i}log\frac{n}{2^i}$$
I am not sure even where to start. I know there is closed form for
$$f(x) = \Sigma_{i=0}^\inf \frac{x}{2^i} = 2x$$, but this does not seem to help really...
How would I find a closed form?
Thanks
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Is the language of panalphabetic strings decidable by DFA? If so, how can I prove it?
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