Mean Definition and 1000 Threads

What does it mean: "transforms like a vector" Reading Zee's new "Einstein Gravity in a Nutshell" I just don't get it what exactly is meant by "transforms like a ...". He explicitly writes that not any odd column of numbers is a vector, so I am trying to figure out what exactly is meant. Here is...

ive only studied up to calculus 2, and have never encountered ∏, but from what i believe it means, it is a multiplier. much like summation but instead of adding things together they are times'd together. is this correct? and also can i see a example? thank you :)

If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)? Thank you!

I haven't studied quantum physics academically and I have no understanding of it mathematically so forgive me if my questions are strange, nonsensical or erroneous. For instance in the double slit experiment when we attempt to observe the object going through a slit then the diffraction...

Can the arithmetic mean of a data set of complex numbers be calculated? if so, can the method be demonstrated?

Hello, Does anyone know why we use the root mean square of the relative velocity in calculating the mean free path? As is done in this example: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/MolecularCollisions.htm Seems like it would make more sense to find the mean of the...

So this is a fairly simple conceptual question: can you estimate/compare the mean free paths for individual components of a mixture of gases? I'm primarily looking at the equation given here and the information accompanying it. Consider the case where we have several individual, separate...

Hello, I've been trying to find online where I could calculate my grade based off a college curve. So the average grade on the test was a 63. The RMS is 16. I got a 86. So what will my grade curve to? This is out of 50 people. Also, the professor curves to a 70 (I think).

...curvatures in spacetime being created by Earth's gravity? My understanding is that its speed offsets the gravity being created by earth, that it's freely falling towards Earth but never hits it because its speed somehow causes it to keep missing. If that's the case, wouldn't that suggest...

Homework Statement Metric ansatz: ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ where: d\tilde{r} = e^{\frac{B}{2}} dr Homework Equations How to calculate second fundamental form and mean curvature from this metric? The Attempt at a...

Hi forums. I have what I think is a simple question but I'm making myself confused. I'm trying to work out the relationship between energy density ( u = energy per unit volume ) and temperature in a multi-species ideal gas (no molecules just different mass ions). The simplest example of...

I found this in Srednicki's QFTbook. I don't know what ↔ means. Help me, please

Homework Statement Two waves travel in opposite direction form a standing wave of y= 2sin(31.42x)cos(7854t). Find the positions of first two nodes with x>0. Homework Equations The Attempt at a Solution The question didn't say whether the standing wave starts from node or...

So in finding a pattern for the nth derivative for y = x-1 the book wrote y(n)(x) = (-1)nn!x-n-1 What does the exclamation mark mean? I know != means not equal to.

Homework Statement find dy/dx for the function xy^2+xlnx=4y for x>o Homework Equations xy^2+xlnx=4y The Attempt at a Solution I found the dy/dx to be "(y^2+lnx+1)/(4-x)=dx/dy" What is it asking me to do with the x>0? Do they want me to plug in a value greater than 0 for x and solve for y...

Hi Guys I normally post over on the Quantum Physics subforum and over there the question came up of if a probability of 1 means a dead cert. I am pretty sure Kolmogrov's axioms imply it but another person wasn't so sure. Here is what he said: 'I think it will be easier to explain this by...

I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))...

So I tend to here something like "(insert famous scientist) mastered calculus at the age of 13". What exactly is that suppose to mean? Surly you can be good at a subject and get an A in the course, but still be far from a master. To those of you who are pursuing higher education or especially...

The book Orbital mechanics by Curtis says that the function (I labeled M2evals) is monotonically increasing. However, at pi, I have a discontinuity and the graph jumps below the negative axis when it should continue on; that is, the e = 0 should be the line y = x. import pylab import...

I have been following Quantum Cosmology since Hawking's A Brief history of Time first appeared. That inspired me to attempt to drill down to the technical papers involved. I also made use of the book by Hawking and Penrose, The Nature of Space and Time. Very broadly speaking there seems to be...

I was taking a test and basically for the answer I had limited it to two choices. A: x=3 and x does not equal 2 or B. x=3 x=2 When I plug in three, I got 3/1=12/4 so three is true. But when I plugged in two I got 3/0=8/0 So would this be true too? Or does x not equal 2? Wouldnt...

eg. Find the directional derivative of the function phi=xyz^2 at the point (1,2,3). Actually what is the math used for? Let's say phi is the temperature of air(scalar field). ∇phi will be the rate if change of temperature at (1,2,3), why the direction come out. directional derivative of it...

Air Compressor: What would "twin-cylinder" mean? I'm figuring out details about an old compressor and it's made by a Greek Company. I can't find too many details but one part that confuses me is it says "twin cylinder". Picture below. Specs say: Oil lubricated twin-cylinder...

Given that a photon of known wavelength is emitted when an electron goes to a lower energy state, if there are only so many different types of atoms, and only so many electron orbits around those nuclei, the number of wavelengths possible is finite: If true, then the EM spectrum is quantised...

I know lots of people say that when you are learning something it is better to understand it rather than just blindly try to memorise it. This might be a silly thread, maybe I'm thinking too hard about it but I would really like some clarification. So I'm wondering, what does it really mean...

Homework Statement State the Mean Value Theorem and find a point which satisfies the conclusions of the Mean Value Theorem for f(x)=(x-1)3 on the interval [1,4]. 2. The attempt at a solution Mean Value Theorem:states that there exists a c∈(a,b) such that f'(c)=\frac{f(b)-f(a)}{b-a}...

Why is brake mean eff.pressure higher at max.Torque than max.power?,I am looking for an explanation in terms of equations,since I already know the theoretical reason i.e at Max.Power→the rpm is at Max for the engine →the friction losses are maximum→bmep at max power is lower than at max.torque...

Let X1, X2, X3 be three random variables. Suppose all three have mean μ and variance 1. The sample mean is Y = (X1 +X2 +X3)/3. (a) Can you compute the mean of Y? If so, what is it? If not, why not? I have that it is either μ OR that it is not possible to find, since we don't know if they...

Homework Statement Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Using the generalised mean value theorem, prove that: f(x)=f(c) + (x-c)f'(c)+\frac{(x-c)^2}{2}f''(\theta) for some \theta \in (c, x) Homework Equations Hints given suggest consdiering F(x) =...

Hello. I have a problem with one task. The task is: Suppose that you playing the game. You have n moves. on each move you win the game with probability p. Your winning amount is equal to move number. For example if you win in first move your winning amount is 1, if you win in n move, your...

Hi, this is my first time posting on these forums but I've been reading them for a while. I was having a look at metamaterials and it mentioned that metamaterials had negative permittivity and negative permeability. I also found that metals naturally had negative permittivity; though I am...

If at 120 K the Vrms is v , then at 480 K it will be a. 1 b. 2 c. 3 d. 4 Which formula is to be used here? Plz solve this.

Also how can local causality be violated?

What does "aqueous workup" mean? I'm taking a second year organic chemistry and it's a slightly advanced level but I didn't take the 1st year advanced level org.chem. so I may have missed a couple of common terms. What I don't understand is what does workup mean? At the end of some reaction...

Hello I was trying to solve this sample problem, but I really don't get it. The book says this word by word: The equation sin3x=1 implies 3x=(pi/2)+2kpi, k an integer. x= (pi/6)+(2kpi/3), k an integer *Divide each side by 3. Because x is not restricted to a finite interval, the given...

Textbooks I've looked into usually follow a sort of "prescription" for quantizing a field theory, which consists of "promoting the fields to operators" and "imposing commutation relations." Is there an English translation of what this means? Like for instance, is this tantamount to taking the...

Homework Statement The problem is to calculate the mean molar mass of the reaktion below, which takes place in a combustion engine. C4H10 + z(0.79N2 + 0.21O2) → αH2O + βCO2 + γN2 where the molar masses for the different molecules/atoms are: MH2O = 18, MCO2 = 44, MN2 = 28, MO2 = 32, MC =...

As you may have noticed, Politics and World Affairs is gone. This is now Current Events, a more lighthearted look at what is in the news. To get started, I saw this article today. WHO THOUGHT THAT WAS A POODLE? I've got to say that is one crazy looking ferret. (The ferret is on the right)...

A polynomial of degree ≤ 2 ? what does this mean. Would it just be a + bt + c t^2 = f(t) Or at^2 + bt + c = f(t) Is there even a difference between the two equations considering the fact that a,b, and c are unknown?

How come Higgs Bosons have mass if Higgs field itself gives other thin How come Higgs Bosons have mass if Higgs field itself gives other thing their mass?

I am a bit confused the concept of energy density. I was taught that, in vacum: \frac{1}{2}\int_{V}^{ } \rho P dV = \frac{1}{2}\varepsilon _0 \int_{V}^{ } E^{2} dV where P is the eletric potencial. This is true because: \rho P=\bigtriangledown \cdot (PE)+E^{2} where the...

Homework Statement "as long as the volume charge density is finite (which is not true of surface charge distributions or point charges), the electric field is continuous. Homework Equations The Attempt at a Solution I know that for surface charges distributions and point charges...

Here is the question: Here is a link to the question: Calculus 1 Help on Mean Value Theorem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

What does it mean if something is rated as 40W?

Homework Statement Suppose X is a normally distributed random variable. Suppose also that P ( X > 44.7 ) = 0.33 and P ( X < 46 ) = 0.7123. What is the mean and standard deviation of X ? Homework Equations The Attempt at a Solution P(X<44.7) = 1-P(X>44.7) = 1-.33 = .67 P(X<44.7)...

http://global.britannica.com/EBchecked/topic/495677/refractive-index refractive index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another. If i is the angle of incidence of a ray in vacuum (angle between the incoming ray and the...

I am reading about the root mean square and Parseval's Theorem but I don't understand how we find $A_0$. So it says the average $\langle x\rangle$ is zero and the $x_{\text{RMS}} = \sqrt{\langle x^2\rangle}$ where $$ \langle x^2\rangle = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2}x^2dt $$ The Fourier...

Hi I found this equation in a machine learning book: "we want to minimize the mean squared error:" $E= \frac{1}{2} \sum_{n=1}^N (y-t)^2$ what I do not understand is the \frac{1}{2} , if it is a mean it should be \frac{1}{N}, why are they restricting to 2? In the text there is no reference to y...

what do we mean by "pure gravity" 1-what we mean by "pure gravity" and "gravity coupled to matter"? 2- why pure gravity characterized by c=0 (c: central charge), and what is the conceptual meaning of central charge regards

Working on some problems that have vectors, for example f(x) = [-x1/|X|3, -x2/|X|3] And then I am asked to find the largest interval of existence. The answer says "E = R2 ~ {0}. I'm not sure what this means. Does it mean the interval of existence is everywhere except 0? Is that what the ~...