What is Independent: Definition and 743 Discussions

The Independent is a British online newspaper that was established in 1986 as a national morning printed paper. Nicknamed the Indy, it began as a broadsheet and changed to tabloid format in 2003. The last printed edition was published on Saturday 26 March 2016, leaving only the online edition.It tends to take a pro-market stance on economic issues. The newspaper was controlled by Tony O'Reilly's Irish Independent News & Media from 1997 until it was sold to the Russian oligarch and former KGB Officer Alexander Lebedev in 2010. In 2017, a Saudi Arabian investor bought a 30% stake in it.In June 2015, the newspaper had an average daily circulation of just below 58,000, 85% down from its 1990 peak, while the Sunday edition had a circulation of just over 97,000. The daily edition was named National Newspaper of the Year at the 2004 British Press Awards. The website and mobile app have a combined monthly reach of 22,939,000.

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  1. A

    Are These Vectors Linearly Independent in R*R?

    Homework Statement determine whether the following are linear independent sets of vectors in the vector space R*R of all functions from R to R a)fn:=1+t+...+t^n for n=1,...4 b) sin,sin^2 ,sin^3 c)1,sin^2,cos^2 Homework Equations The Attempt at a Solution can i do like this for...
  2. S

    An independent Physics study, group for all levels

    There are a wealth of resources... videos, texts, libraries, etc. that are available to us in our studies in physics. Even Physics Forums sections devoted to compiling lists of such resources! For the sake of pacing, discipline, and other reasons (guidance?), who else would be interested in...
  3. B

    That these events are independent?

    I was wondering, if you are told that for two events A and B, We Have P(A)=0.4 and $P(A\mid B) = 0.4$\\ Can you assume as P(A) = P(A\mid B) That these events are independent? regards Brendan
  4. E

    Independent statistics: Basketball?

    Hi, I'm a bit stuck on this problem A basketball player misses 30% of his free throws. He ends up in a situation where he has the potential to shoot two penalty shots if and only if he lands the first shot (called a one and one, I believe). The outcome of the 2nd shot is independent of the...
  5. C

    Independent Events Question: Coin Tossing

    Hello all, I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated. A fair coin is...
  6. C

    Prove Au and Av Linearly Independent

    Homework Statement Let u_1...u_n be linearly independent column vectors in R^n and A an invertible n x n matrix. Prove that the vectors Au_1...Au_n are linearly independent. Homework Equations The Attempt at a Solution It is easy to prove this using scalars and the definition of...
  7. F

    Are the Vectors (1,x) and (1,y) Linearly Independent in R^2?

    Homework Statement When are the vectors (1,x) and (1,y) linearly independent in R^2? When are the vectors (1,x,x^2), (1,y,y^2), and (1,z,z^2) linearly independent? Generalize to R^n. The Attempt at a Solution At first, I think I misconstrued the question and I ended up finding basis...
  8. V

    Proving that g1,g2,g3 are linearly independent

    Homework Statement Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e^{}x, g2(x) = e^{}2x and g3(x) = e^{}3x. Show that g1, g2 and g3 are distinct.Homework Equations If g1-g3 are linearly independent, it means that for any constant, k in F (field) then...
  9. D

    Independent and Dependent Variables

    I'm doing a lab where i need to calculate the heat energy, or enthalpy using the equation (delta) H = m x c x T my reactions are going to be of a strong acid and a strong base: Sulfuric Acid + Sodium Hydroxide→ Sodium Sulfate + Water and of a wek acid and the same strong base...
  10. M

    Decomposition of a R.V. into dependent and independent parts

    Given random variables X and Y, which are not independent, is it always possible to find a random variable W which is independent from X, such that Y = f(X,W), for some function f? Example: let the joint distribution of X and Y be Y 0 1 X+------- 0|1/3 1/6 1|1/6 1/3 Then if we...
  11. D

    Combining independent probabilities in a meaningful way

    I have 1000 experiments on the same data, each of which is trying to decide the probability that the data agrees with a model. The problem is, even if each experiment REALLY agrees with the model (ie. p(d1) = .99, p(d2) = .99, etc), when I multiply these together to get P(d1 & d2 & d3... &...
  12. I

    Time independent perturbation theory

    Homework Statement Assume that H0 describes a paramagnetic system that couples to a magnetic field via the Zeeman effect, i.e. V = −μB, where μ is the magnetic moment. Note that for the unperturbed paramagnetic system the probability of having an up-spin is equal to that for a down-spin. Show...
  13. B

    What happens inre time if a clock is independent of the motion of its reference body?

    Einstein wrote ... Q: What would happen inre (in regards to) time if, for any reason, a clock were to be 'independent of the state of motion of [its] body of reference'? A: _____ (?)
  14. L

    Are These Vectors Linearly Independent?

    Homework Statement Given vectors: a1 = (1; 2; 0), a2 = (2; 1; 3), a3 = (0; 3; -3). Find out if these vectors are linearly independent. Homework Equations The Attempt at a Solution \begin{cases}...
  15. O

    Are Column Vectors in AB Unchanged if Linearly Independent?

    If you have a 3x3 matrix AB of rank 2, and you are asked to find two linearly independent vectors in the column space of A, are those the same vectors in the column space of AB? I figure it is since if the vectors are linearly independent they wouldn't change. Am I right?
  16. S

    Can two independent sources of light be coherent?

    Can two independent sources of light be coherent?
  17. M

    Linear Algerba - Finding linearly independent vectors

    Hi guys, I am solving a problem in the form: (ATx=0 where A is a matrix of known numbers and I am solving for x. After performing reduction and multiplying ATx, I am left with the following equations: -X1 + X4 - X5 = 0 -X2 + X4 = 0 -X3 + X4 -X5 + 28X6 = 0 From these equations, I...
  18. H

    What kind of knowledge do independent inventors have?

    What kind of knowledge do independent invent0rs have? Do they have knowledge in all the areas of engineering? Thanks!
  19. Q

    Book for Independent Study in Modern, Thermal, or Mathematical Physics?

    I'm looking to do a guided independent study course at my college next term; the college doesn't offer physics beyond the introductory calculus-based sequence, which I've completed, and I'm not yet ready to transfer. The physics major sequence at the school to which I intend to transfer...
  20. N

    Maths / Physics - How to approach independent learning

    Hi everyone, I know this subject has been broached before but would appreciate some extra help - I'm an English major in second year uni so I haven't done physics and maths for a while, but I have quite a lot of free time at the moment and would really love to get back into these subjects...
  21. I

    Maxwell Equations when current density is time independent and divergence free

    Homework Statement If the current density is time independent and divergence free, show that the Maxwell Equations separate into independent equations for \vec{E} and \vec{B}. Homework Equations Maxwell's equations The Attempt at a Solution The only Maxwell equation with \vec{j}...
  22. J

    Linearly independent vectors and span

    So the question is... Let v1, v2,...,,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot span V. I honestly have found myself completely lost lately and I suck at writing proofs. So this is what I see, v1, v2,..., vn is linearly independent iff...
  23. R

    Correlation with two independent variables

    I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y) =E(XY^2)-E(X)E(Y)^2. If X and Y are...
  24. S

    Are the epsilons independent from each other?

    \varepsilon _t = z_t \sigma _t z_t \sim IID\,N\left( {0,1} \right) \sigma _t^2 = f\left( {\sigma _{t - 1} ,z_{t - 1} } \right) Are the epsilons independent from each other? Why?
  25. G

    If nuclear forces would be spin independent

    If nuclear forces would be spin independent! HI all,a question was asked by my teacher that "if nuclear forces would be spin independent then how many types of DEUTRON would be existing and what would be their relative abundances. Please help Thanks
  26. N

    Independent Research Project Need Help

    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...
  27. K

    Independent or paired? (Statistics)

    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 I also did a 95%...
  28. B

    Find 2 linearly independent eigenvectors and a eigenvalue

    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...
  29. J

    External gravity field independent of mass distribution?

    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...
  30. D

    Complex conjugate variables as independent variables in polynomial equations

    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...
  31. J

    Linearly Independent Solutions[help please]

    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...
  32. H

    Force mechanical oscillator and frequency independent?

    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...
  33. L

    Distribution of two independent exponential random variables

    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...
  34. A

    Conditional probability using dependent and independent tests

    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"...
  35. C

    Complex conjugate an independent variable?

    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...
  36. P

    Linearly independent but not orthogonal, how come?

    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.
  37. S

    Independent Learning [relativity books]

    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...
  38. C

    Independent components of tensor

    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.
  39. P

    Independent / Dependent variables for implicit functions

    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?
  40. S

    Linearly Independent Columns of a Matrix

    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...
  41. N

    Independent and interacting electron models

    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.
  42. A

    Why is this linearly independent?

    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...
  43. B

    Independent research: Is it possible?

    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?
  44. maverick280857

    Are max and min of n iid r.v.s. independent?

    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
  45. Somefantastik

    Independent identically distributed random variables

    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?
  46. F

    A solution to time dependent SE but not Time independent SE?

    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...
  47. E

    PROOF: Independent vectors and spanning vectors

    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.
  48. E

    Ideal Gas Law: Exploring Independent Variables

    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...
  49. P

    Probability with independent outcomes

    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...
  50. P

    Probability of Getting Red at Least Once in Two Spins of a Wheel with 8 Colors

    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...
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