Independent Definition and 713 Threads

Are the functions y=0 and y=sinh(pi*x) linearly dependent or linearly independent on the intercal x>0? I'm not sure what I'm supposed to do here, but I try to divide them: 0/sinh(pi*x). This is certainly 0, since sinh (pi*x) is positive when x>0. Since 0 is a constant, the functions must...

I'm looking ahead to winter quarter 2008 when I will be starting an independent research project. I wanted to get an early start in thinking about what I might be able to do. I am thinking that I want to do something in signal processing, but don't have enough knowledge to make a choice. Here...

Dear all, I wonder wheather there exsits a probability inequality for the sum of independent normal random variables (X_i are i.i.d. normal random varianble with mean \mu and variance \sigma^2): P\left(\frac{1}{n}\sum_{i=1}^n X_i - \mu> \epsilon\right)\leq f(\epsilon, \sigma^2,n) \right). We...

hey everyone, I first started doing independent research myself, exploring topics myself, but how do I do "offical" research that counts towards college admissions (I am a high school student by the way). Thanks

I'm currently reading Griffith's book on time independent Schroedinger's equation about delta functions. However, I complete dislike how the book deals with the delta distribution. firstly, the book discusses how to solve: -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}-\alpha\delta\psi=E\psi for...

Is this a valid thing for society to aim for? Would this do more harm than good? Technology is capable of taking us towards this.

I have looked all over in many textbooks and I cannot find a decent explanation of this. Most textbooks simply say that it is independent of applied bias because all of the minority carriers generated by thermal energy within a diffusion length of the depletion region will essentially get swept...

Question: Prove that the list (x^3, sin(x), cos(x)) is linearly independent in V (V being the vector space of real-valued functions. In other words... common everyday math) They're linearly independent, its pretty obvious. The issue is -- proving rigorously. This is not for an assignment, its...

I’m student at the University of Arizona. In my political science class, I need to use SPSS to calculate bivariate correlation between a categorical independent variable (Presidential or Parliamentary system) and a continuous dependent variable (various measures of democracy) I’m using the...

"Independent Continuum" Can anybody please explain to me what this actually means. My understanding in very vague terms is that something is constant, with reference to Einstein's The Special and General Theory book, where he says that we often think of time (and space i think) as "independent...

Marcus! Your find... http://arxiv.org/abs/gr-qc/0703097 New directions in Background Independent Quantum Gravity Fotini Markopoulou Perimeter Institute for Theoretical Physics Good stuff. How influential is Fotini Markopoulou? Is anybody going to listen? jal

Hello, I am not sure if this is the right place to ask this, but I don't readily see a "numerical methods" forum here so I assumed this would be the place to go. Sorry if I overlooked another place to post this! Anyway, I have some points interacting via potentials that are dependent only on...

Homework Statement Let \mathscr{X} be a set, \mathscr{F} a \sigma-field of subsets of S, and \mu a probability measure on \mathscr{F}. Suppose that A_{1},\ldots,A_{n} are independent sets belonging to \mathscr{F}. Let \mathscr{F}_{k} be the smallest subfield of \mathscr{F} containing A_{1}...

let V be a vector space and K a nonempty subset of V prove/disprove : K is linear independent set iff for every T such that T is a proper subset of K, span(T) is a proper subset of spanK. im having difficulty finding a counter example, so i think this statement is correct, but how to prove...

My teacher gave these notes: In general, if any two events A and B we find that Pr(B|A)=Pr(B), or equivantly, Pr(AnB)=Pr(A)Pr(B), then the events A and B are independent. but i thought that when A and B are independent then Pr(AnB)=0? what is my teacher trying...

A friend gave me this problem; it's been years since I've taken probability, and I'm really rusty. I'm curious how to solve it. Suppose you have a normal pdf with mean mu and stdev sigma that represents the distribution of test scores. What's the probability that two randomly selected...

I found this post somewhere on the net. I am also getting a similar problem. Can you all please help? +++++++++++++++ I have a problem, I try to solve but still get stuck. Can you please read my solution and point out what my wrong points are? Xn is a Markov Chain . n=1...M. with...

I'm having trouble understanding what to do for this problem. The question I'm trying to answer is: Find 3 linearly independent solutions to the following differential equation, y^(3) + 3y'' + 3y' + y = 0. I really don't know how to even start this problem and what I'm really looking for. I...

Greetings.Let me tell you a little bit of my story When I started school a year and a half ago I was pretty sure that I wanted to become an engineer. I really like the concept of the computer as a the ultimate comunication and calculation tool, and I've always have an interest in...

Hello, I had this problem to do for statistics. I am pretty sure I did the first two parts correct. The third, I am not so sure about. I'd appreciate and guidance. A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume...

Hi everyone, I would like to seek help in proving that the vector space postulate 1.X = X cannot be derived from the other postulates, e.g. X + 0 = X, X + (Y + Z) = (X + Y) + Z. The only hint I am given is to construct the "pseudo-scalar product" c # X = the projection of c.X on a fixed...

Don't miss this paper from the Zeilinger group: R. Kaltenbaek et al, PRL 96, 240502 (2006). In particular, read the first paragraph: Zz.

A question on a General Relativity exam that I have asks how many linearly independent Killing fields there can be in an n-dimensional manifold. I'm sure I've seen this question before and I think that the answer is n(n+1)/2, but I can't remember why! Any help?

How many independent components are there to describe the EM field? The six in the field tensor, the four in 4-vector potential or the two when Coulomb gauge is being used? thanks

I don't know if this is a rule, but can a set of vectors be linearly independent if their determinant is not equal to zero? say 4 vectors are given in R^4, if I took the determinant of the 4 vectors such that det{v1 , v2, v3, v4} is not equal to zero, could i say that these vectors are...

Just like above, is it?

Original here : http://www.everything-science.com/content/view/155/2/ After reading this , a question sprung into my head : "Where are they going to get that much Hydrogen , to replace all the fossil fuels that are used today ?" Any ideas ?

I picked number 2. Just so you get a sense of how my comments relate to the poll. I'm curious to know what brings happiness to the members here at PF. I have got into many conversations with people where they think my views are just insane and flat out stupid. I believe happiness is...

Find a linearly independent set of vectors that spans the same subspace of R^3 as that spanned by the vectors \left(\begin{array}{c} -2 & -1 & -2 \end{array}\right) , \left(\begin{array}{c} -2 & 3 & -8 \end{array}\right) , \left(\begin{array}{c} 0 & -2 & 3 \end{array}\right)...

Here is a trig question that I've been thinking about. I want to know which one would be the independant and the dependant of the points (r , theta)

Now, my textbook says that force of friction is independant from the area of contact. But, when the tyres of my bicycle get deflated i have to exert extra force than otherwise. Why?

This seems to be the goal expressed most clearly at Loops '05. it is a slight redirection or change in emphasis in the common program. Matter should naturally occur in quantum gravity. It's explicit. two leading talks in this regard were by Rovelli and Freidel In the latter's talk, Feynman...

Time Independent Rotational Kinematics equation? [FONT="Tahoma"]Ok i was trying to figure out the angular acceleration for a problem, but i didn't have the time...so the book said to use the "time independent rotational kinematics equation" but i couldn't find it in the book anywhere or even on...

How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions. One is given that the Riemann tensor is an (2,2) irreducible rep of GL(4, \mathbb{R}) and obeys Bianchi I R_{[\mu\nu|\rho]\lambda}=0 Been trying this problem for 3 days and...

I am working with a complex scalar field written in terms of two independent real scalar fields and trying to derive the commutator relations. So, \phi = \frac{1}{\sqrt{2}} \left(\phi_1 + i \phi_2) where \phi_1 and \phi_2 are real. When deriving...

The Lagrangian of a system is given by: L = T - V, T = kinetic energy of the system, V = potential energy of the system. L is a function of the generalised coordinates for a system of N particles given by: L = L(q_1, q_2, ...,q_{3N},\dot{q_1}, \dot{q_2},...,\dot{q_{3N}}, t) Suppose L is...

Heard on the news that G.W.Bush was going to let a committee investigate why the help to New Orleans was so ineffective, and what could have been done better. This sounds like a perfectly good idea. However they also claimed that he would lead this committee by himself! :bugeye: Is this true?

Hi I'm wondering if someone can help me out on this question as to how to go about doing it: X_1, X_2... X_7 are independent random variables represnting a random sample of size 7 from the normal N(10, 7) distribution. Find to 3 dp probablitity that the sample total exceeds 88. I tried to...

:confused: I am sooo intrigued. The speed of light is independent to the speed of the observer. Why? I don't understand and is it the speed of light only that is independent to the speed of the observer? What makes it so special?

What is the relationship between the number of branch points and the number of independent current in a circuit?

Hello my question is not academic based just personal. I wanted to know if an event as a probability of P of occurring per day and it occurs everyday for a week. Then, for the week the probability is P? i.e. The probability of picking the correct number in a dice roll is 1/6. Then at...

Hello. I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an undergraduate level. Thanks a bunch! -Tim

Given y1=3t, y2=|t|, determine whether the given pair of functions is linearly independent or linearly dependent. I can't do the Wronskian on this one since y2 is not differentiable at 0, is there any other way to do this?

prove if {v1,v3}, {v2,v3}, and {v1,v3} are all linearly independent, then{v1,v2,v3} is not linearly independent. I'm having trouble showing that is true other than showing a counter example when it doesn't work, namely when v1=1,v2=0, and v3=1. TIA.

I have a question about independent random variable: Let say we flip a fair coin, the set of outcome is S={H,T}, P(H)=1/2, P(T)=1/2. Define random variable X:S->R by X(H)=1, X(T)=-1. From what I read in books, I can define X1 and X2 as independent identically distributed (iid) random variables...

Let V=C[0,1] be the vector space for all-real valued continuous functions on [0,1]. If X={1,cosx,cos2x, cos3x, cos^2x, cos^3x}. How do I find a maximal subset of X?

Hello out there. I'm working on a proof by induction of the Wronskian and need a little boost to get going. So, here goes: If y_1,...,y_n \in C^n[a,b], then their Wronskian is...

Hi I'm presented with a set of vectors in \mathbb{R}^{3} v_1 = (a_1,a_2,a_3) v_2 = (b_1,b_2,b_3) and v_3 = (c_1,c_2,c_3) I'm suppose to determain if these vectors are linear independent. My question is: The most simple way of proving the above is that written the vectors as a...

f1(x)= (sqrtx) + 5, f2(x)= (sqrtx) + 5x f3(x)= x-1 i don't know how to start

What goes into an independent study? I need to take one this summer to take a math course that isn't offered then, but I'm not really certain what it involves. Do I study on my own and show up periodically to take exams? Or do I receive one on one instruction from a professor for a few hours a week?