Independent Definition and 713 Threads

I am in a senior level scientific measurements using digital interfacing class, which is basically like a smash-up of digital circuits lab, intro to DAQ and DAC/ADC, and senior project. Now, part of this class, only 10%, is a independent "research" project. I put this in quotes because we only...

[FONT="Century Gothic"]I was just doing some revision and came across a sticky thought - Suppose you got two appraisers for 9 car damages and both give different prices for the repair. Would the samples be independent or paired? I reckon it's paired but I can't put a reasoning behind it! And...

Hi I am supposed to, without calculation, find 2 linearly independent eigenvectors and a eigenvalue of the following matrix A 5 5 5 5 5 5 5 5 5 The eigenvalue is easy -- it is 15. And I can find one eigenvector, [1 1 1] (written vertically), but another without calculation? Is there...

Hi. Gauss' law applied to gravity states that the gravitational flux through a given surface is proportional to the total enclosed mass. Considering a gaussian surface which encloses a continuous mass distribution, an arbitrary re-distribution of the total mass must yield the same value...

Hi, Is there any trick to treat complex conjugate variables in polynomial equations as independent variables by adding some other constraint equation ? Say, we have polynomial equation $f(x,x^{*},y,...) = 0$. where x^{*} is the complex conjugate of variable $x$. I might think of taking $x = r...

1. Homework Statement Find two linearly independent solutions valid for x>0 xy''+y=02. Homework Equations well first of all, all the solutions that i get to see in the forums is interms of the euler formula.. but in the course that I am taking(advanced engineering mathematics), it is...

i got these question which i do not know how to do... Qn. In a forced mechanical oscillator, show that the following are frequency independent. i) the mechanical amplitude at low frequencies. ii) the velocity amplitude at velocity resonance. iii) the acceleration amplitude at high...

Q: If X_1 and X_2 are independent exponential random variables with respective parameters \lambda_1 and \lambda_2, find the distribution of Z = X_1 / X_2. Discussion The best method to attack this problem apparent to me is coming up with a cumulative distributive function for Z and then...

Hi, I'm trying to work out a probability value from a number of distributions (tests), it gets a little complicated because some of the tests are dependent on each other. Lets say I have a surface which has black and white regions distributed over it, where black is "true" and white is "false"...

It's very commong to use z and z* as two independent variables, differentiating with respect to one while keeping the other constant. Can you please give me some intuitive insight into this method, and why it works so well? Because every time I see this my first thought is that z and z* are NOT...

Hi everyone, I was reading about Gram-Schmidt process of converting two linearly independent vectors into orthogonal basis. But, as I understand, if two vectors are linearly independent then they are orthogonal! isn't that right?? Could anybody explain... please.

Hello everyone, summer break has begun for me, and I was wondering which way is the best possible way to learn new stuff over the summer, I wanted to dive into, and kind of begin, to have an understanding of Lorentz Transformations and Einstein's special relativity theory, is there any book or...

Homework Statement For indices running from 0-3: R_{iklm} = -R_{kilm} = -R_{ikml} With the above conditions how do I know the number of independent component is reduced from 4^4 = 256 to 36. No idea how to figure this out.

This probably has a really simple answer. Forr u=x^2-y^2 and v=x^2+y^2 x and y are apparently the dependent variables. But the independent variable is the input while the dependent variable is the output, so since u=f1(x,y) and v=f2(x,y) shouldn't they (u and v) be the dependent variables?

Hi wondering if can anyone help me... I've gotten so bogged down in all the rules and stuff for singular/non-singular matrices I've completely confused myself! Can anyone tell me is it true to say that if I have a matrix P, det(P) is NOT EQUAL to 0, then the vectors that would form the...

Why is it that we can treat electrons as independent and non-interacting in solid state physics? What is the difference between mean-field theory and density functional theory? In lame terms please.

Homework Statement Determine whether the given vector functions are linearly dependent or independent on the interval (-\infty, \infty) \begin{pmatrix} t \\ 3 \end{pmatrix}, \begin{pmatrix} 4 \\ 1 \end{pmatrix}Homework Equations The Attempt at a Solution I computed the wronskian to be t-12...

Looks like I will not have any research opportunities this summer. However , could I conduct my own research indepedently without working in a professor's research group?

Hi Suppose X_{1}, \ldots, X_{n} is a sequence of i.i.d. random variables. We define X_{(n)} = max(X_{1}, \ldots, X_{n}) X_{(1)} = min(X_{1}, \ldots, X_{n}) Are X_{(n)} and X_{(1)} independent? Whats the best/easiest way to verify this? Thanks Vivek

For two independent and identically distributed random variables having the exponential distribution, do they have the same lambda value, or are the lambda values different?

A solution to time dependent SE but not Time independent SE?? How is it possible that a wave function is a solution to the time dependent schroedinger equation, but not to the time independent schroedinger equation (without time factors tacked on) with the same potential? I had this case on my...

Proof: 1. why you need at least m vectors to span a space of dimension m. 2. If m vectors span an m-dimensional space, then they form a basis of the space.

Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/7A20B047-A049-44D6-96D2-75602F179856/0/notes_dfnitns.pdf There it says tht the number of independent variables of a simple fluid is 2 (see the "Complete Specification" section). But the ideal gas law is PV=NkT which...

Jeeserssweesers(for a lack of a better word), probability is confusing. Homework Statement A family has three children, no twins or.. that same just with three. a| What is the chance that all the children are girls. Homework Equations The chapter here shows the equtations...

uh, I mean probability with independent outcomes, heh. Homework Statement A wheel I'm spinning twice has 8 different colours(among them the colour red). It will then give two different outcomes. Q: What is the probability that the outcome will give the colour red at least once. The...

Hi I have a question regarding i.i.d. random variables. Suppose X_1,X_2,\ldots is sequence of independent and identically distributed random variables with probability density function f_{X}(x), mean = \mu and variance = \sigma^2 < \infty. Define Y_{n} = \frac{1}{n}\sum_{i=1}^{n}X_{i}...

Why does this work?? (X and Y independent) There is an image attached to refer to my question. A ballistics cart traveling at constant velocity can shoot a projectile straight into the air and the projectile will be caught in the car when it lands because of the independence of the X and Y...

Homework Statement Given x_{1}= \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, x_{2}= \begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}, x_{3}= \begin{pmatrix} 2 \\ 6 \\ 4 \end{pmatrix} Find the dimension of Span(x_{1}, x_{2}, x_{3}) Homework Equations If V is a vector space...

Hi Ho! If y=\sin x, \frac{dy}{dx}=\frac{d(\sin x)}{dx}=\cos x. If x=\sin y, y=\arcsin x, and therefore \frac{dy}{dx}=\frac{d(\arcsin x)}{dx}=\frac{1}{\sqrt{1-x^2}}. But, if x=\sin y, can \frac{dy}{dx} be done as \frac{dy}{dx}=\frac{dy}{d(\sin y)}=\frac{1}{\frac{d(\sin...

Homework Statement A particle of mass m and energy E, where E >V1 >V2 travels to the right in a potential defined as V(x) = V1 for - b < x < 0 V(x) = 0 for 0 < x < a V(x) = V2 for a < x < b (a) Write down the time-independent Schrodinger eq. and its general solution...

Show that the evaluation of the pullback of a constant 1-form k_{1}dx + k_{2}dy + k_{3}dz over the directed line segment from \bold{r} to \bold{s} does not depend on which linear parameterization is chosen. So (x,y,z) = \bold{r} + t(\bold{s}-\bold{r}) . Then what?

Apparently next week, Kosovo, the small southern povince of Serbia is set to declare independence, which will become a reality if the EU and US recognize it. Of course, Serbia and Russia disagree. In Kosovo, it's 'Independence Eve'...

Hi all, assume we have a sample space with 2^n points. (it size is 2^n for some natural n) I need to prove that the maximal number of independent binary (indicator) random variables (which are not trivial, i.e. constant) is n... Thnks, Pitter

I'm not sure how to get started with this: Suppose you have two independent poisson processes, X ~ Po(Lambda1) Y ~Po (Lambda2). How would you figure out the probability of one coming before the other? Thanks

Say f is a continuous function on R. How could I find two linearly independent solutions of (y' + f(x)y)' = 0? Notice that there is no hypothesis about f being differentiable, so the obvious method of attack (taking the derivative of each term in the parenthesis and working off the resultant...

[SOLVED] Change of independent variables Homework Statement x = cos\theta Show (1-x^2)\frac{d^2y}{dx^2} - 2x\frac{dy}{dx} + 2y = 0 becomes \frac{d^2y}{d\theta ^2}+ cot(\theta) \frac{dy}{d\theta} + 2y = 0 Homework Equations The Attempt at a Solution dx = -sin(\theta) d\theta ... As a total...

[SOLVED] QM: system with two lin. independent states Homework Statement Imagine a system with just two linear independent states: |1>=(1,0) and |2>=(0,1) (these are actually column matrices, but I don't know how to type those in tex) |\Psi>=a|1>+b|2>=(a,b), also |a|^2+|b|^2=1 suppose the...

independent research - hockey Homework Statement I have been assigned a physics project to do over the break. I need to research the design and use of a piece of protective equipment - I have decided on hockey equipment. 2. The attempt at a solution The most obvious feature is that the...

I have a final tomorrow. Can anyone guide my through this proof? I know i have to wirite the set of vectors as a linear combo, but what can I do nect? Prove that any set of vectors containing the zero vector is linearly dependent.

qestion regarding independent study! Hi everybody! Next semester i am taking the university physics 203 along with linear algebra and differential equation. In the physics class we are studying basic optics, thermodynamics, waves, introductory relativity, and basic modern physics. Although...

When we say that the the velocity of light, c, is independent of the velocity of emitter or the observer, does it mean that .. if we are in an spaceship and measure c with Fizeau arrangement we will obtain the same result, no matter the velocity of the spaceship nor the velocity of the...

How do you see things shaping up during the next few years in Quantum Gravity? the last two years have seen a lot of change there are some new approaches that have either just been discovered (like Smolin's group finding matter degrees of freedom in spin networks) or have recently become...

H=H0 + lambda * W lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0. More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0. I don't understand what is the meaning of " the matrix...

Homework Statement Let X,Y be two independent normal N(0,1) and N(0,2) variables, and Z=XY. Suppose that E(X^4)=3 a) Compute Var(X), Var(Y), Var(Z), Cov(X,Y), Cov(Y,Z), Var(X+Y), Var(X+Z) b) By computing E[(X^2)(Z^2)], prove that X,Z are not independent.Homework Equations Var(X)=E(X^2)-E(X)^2...

H=H0 + lambda * W lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0. More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0. I don't understand what is the meaning of " the matrix...

http://garciarussellchem.angelfire.com/Photo/Change_of_independent_variables_problem.jpg Homework Statement Homework Equations See Image at above adress The Attempt at a Solution See image at above adress

This is my second class in intro to probability at a university level. 1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10. a) Now what is P(pick 1 girl and 1 boy)...

Right now I'm doing Centroids in my math class. we are given two functions. X=-y and X=2y-y^2. My question is, how do I graph these two functions on my TI-89 titanium. The Y=editor is displayed as y(x). Is there a way to change it to X(y). I was able to plot it out on paper, but I use...

Homework Statement Is {(1,4,-6), (1,5,8), (2,1,1), (0,1,0)} a linearly independent subset of R^3. Justify your answerHomework Equations The Attempt at a SolutionI asssumed a(1,4,-6) + b(1,5,8) + c(2,1,1) + d(0,1,0) = 0 then i set up the system a + b + 2c = 0 4a + 5b + c + d = 0 -6a + 8b + c...

Is there any theory of information that considers a 'bit' to be something that only exists relative to a pair of systems exchanging information? I.E there is no such thing as an isolated 'bit'.