# What is Independent: Definition and 744 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.

View More On Wikipedia.org
1. M

### Linearly independent vs dependent functions

For part(b), My solution is, ##(c_1, c_2, c_3, c_4) = (c_1, 5c_1, -c_1, -3c_1)## They have taken the case that c_1 = -1, which gives their expression for a linear dependent function as they have shown. However, I'm confused that the functions are linearly dependent for any value of ##c_1 \in...

22. ### Circuit Analysis Theorem For the Number of Independent Equations

I attached a screenshot of the book (sorry no pdf available for this book). Right above the somewhat central line they give the theorem that if there are m currents and n nodes, then there will be n - 1 independent equations from the current law and m - n - 1 from the voltage law. I count 4...
23. ### Problem with independent events in possibilities

Summary:: problem with independent events in possibilities A forest has a fire per year with probability 30% and it has 2 fires per year with possibility 5%.The probability of 3 or more fires is 0%.The forest might have disasters from the wind which blows with probability of 100% or has...
24. ### I Sum independent normal variables

(I know how to prove it). Prove that a finite sum of of independent normal random variables is normal. I suspect that independence may not be necessary.

28. ### Engineering Step response of RC circuit with independent voltage and current sources

Dear PF, In the figure down below is Q7.47 which asks to determine the voltage v(t) across the capacitor for t > 0. Since it is given that V(0) = 0 there are two scenario's which is between time interval 0 < t < 1 and t > 1 according to the independent sources. For the scenario 0 < t < 1 the...
29. ### A Matrix multiplication, Orthogonal matrix, Independent parameters

Matrix multiplication is defined by \sum_{k}a_{ik}b_{kj} where ##a_{ik}## and ##b_{kj}## are entries of the matrices ##A## and ##B##. In definition of orthogonal matrix I saw \sum_{k=1}^n a_{ki}a_{kj}=\delta_{ij} This is because ##A^TA=I##. How to know how many independent parameters we have in...
30. ### Engineering Circuit Analysis -- How many independent equations can be written using KCL?

I think there are 4 essential node. So we can write 3 KCL independent equations.
31. ### Other How Can I Independently Conduct and Publish Research in Theoretical Physics?

Hi everyone , I have done Bachelor's in Physics from Delhi University , India . I discontinued Master's from Indian Institute of Technology more-than-1 year before completion , it was 2 year course. I want to do research in Physics independently and publish ground-breaking...
32. ### Three independent random variables having Normal distribution

Let ##X_1 X_2 X_3 ## be three independent random variables having Normal(Gaussian ) distribution, all with mean ##\mu##=20 and variance ##\sigma^2##=9. Also let ##S=X_1+ X_2 +X_3## and let ##N## be the number of the ##X_i## assuming values greater than 25. ##E\left[N\right]##=? I did not...
33. ### I Are Intensity and Magnitude independent of the radius of a star?

For a star.. Apparent Magnitude = -2.5log10 I K And I = I0/d^2 So in terms of I0... Apparent Magnitude = -2.5log10 (I0/d^2) And the Stefan-Boltzmann law says: Energy Flux = Sigma(T^4) In my reading it says that Intensity is the energy emitted per unit of area per unit of time. It says the same...
34. ### Independent parameters of the rotation tensor ##R_{ij}##

I am afraid I had no credible attempt at solving the problem. My poor attempt was writing the matrix ##\mathbb R## as a ##3 \times 3## square matrix with elements ##a_{ij}## and use the matrix form of the orthogonality relation ##\mathbb R^T \mathbb R = \mathbb I##, where ##\mathbb I## is the...

50. ### Determining the voltage polarity of the independent current source

I am so sorry if I am posting this in the wrong forum; it is just not a homework problem, and I can't find the right place - it's more of a study help question.