Independent Definition and 713 Threads

Homework Statement Let a system of forces (F1,...Fn) act on a body at points (x1,...xn) respectively. Assume that the resultant or net force vanishes (sum of forces = 0) Show that the resultant torque of this system is independent of the choice of origin, i.e. for 2 different origins x0...

Homework Statement E1 and E2 are two independent events. The probabilities of an error in judgement by a person regarding E1 and E2 are 0.02 and 0.05 respectively. Find the probability that the person will take the correct decision regarding : only one event Homework Equations Two events...

Should the time independent Schrödinger equation contain a differentiating 'd' as shown here: http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html or a differentiating curly 'δ' as shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html Thank you!

Homework Statement Okay so I was given this question to start calculating error on other problems. Consider the equation F(x,y,z) = x^4+2y^3+5yz+5. Let the uncertainty in x be represented by the variable dx, the uncertainty in y be represented by the variable dy, and the uncertainty in z...

Convection heat transfer rate decided by Newton's cooling law doesn't have a relative velocity between the fluid and the solid surface term. But intuitively doesn't blowing faster on a hot surface make it cool quicker?

I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...

I am curious about the proof of the fact that the value of a determinant computed using the Laplace (or cofactor) expansion is independent of along which row (or column) the expansion is performed. Is this a very difficult proof? My textbook omits it entirely. I was curious if someone could...

Homework Statement I need to find the current through the 3V voltage source: picture of the circuit and the equations there: vantraveller.blogspot.ca The Attempt at a Solution I was about to get 3 equations, however, I find myself having 5 unknowns, what other equations can I write...

Forgive me ahead of time, I don't really know how to use LaTeX, (it's on my to do list). Homework Statement Given the vector space C([0,pi]) of continuous, real valued functions on the given interval, as well as the inner product <f,g>=integral(f(t)*g(t))dt from 0 to pi: a) Prove the set...

In a class at OCW 8.01 Professor Walter Lewin said... "...there are very prestigious physicists who even nowadays do very fancy experiments and they try to demonstrate that the time for an apple to fall does depend on its mass even though it probably is only very small, if it's true but they...

Hi, I am trying to identify the independent and dependent variables in the following experiment: Two groups of patients (Epileptic and Normal) are exposed to varying wavelengths of light and their neural response is quantified and recorded. I am using...

Hey, I was wondering if you guys could offer any course guidance on independent studies I could try to take my senior year. I have some ideas, but I was wondering whether you guys could give me any recommendations/book recommendations. My background: I initially wanted to go into a more...

Hello, hopefully this is the right place. This is a homework question, so it should definitely be in this forum, but I wasn't sure which sub-forum to put this rather elementary stats question. Homework Statement In my introductory mathematical statistics class, we've been given the...

Hi PF, I have always wondered what was meant when my teachers told me that a vector is the same no matter what coordinate system it is represented in. What is it exactly that is the same? I mean the components change. So the only thing that I can see remains the same is the length of the vector...

Hello everybody I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent. My attempt : f(x) = k1 * e-t + k2 * e-it + k3 * et + k4 * eit f '(x) = k1 * -e-t + k2 * -ie-it + k3 * et + k4 * ieit f ''(x) = k1 * e-t + k2 * -e-it + k3 * et + k4 * -eit f(0) =...

Hi, I want to whether there is a function (/matrix) such that it can generate a m-dimensional vector such that this generated vector will always be linearly independent of the set of vectors the function has already generated. My problem can be written in pseudocode format as follow. I...

I don't know how to write out matrices nicely on this forum, but suppose you have some matrices:[1 0 3] [2 0 4] [0 0 5] This would, by definition, be linearly dependent, spanning a plane in r3..is this correct? Since c1=0, c2=anything, c3=0 where c1v1+c2v2+c3v3=0 With this: [1 0 3 5] [3 0...

This is about "double slit" setup only without slits and instead there are two electron beams. I found some experiments doing something like this, but the setup was always rather complex, with some mirrors and such. So the question is why can't we get interference pattern by simply crossing two...

Homework Statement ψ(x)=A((2kx)-(kx)^2) 0≤X≤2/k ψ(x)=0 everywhere else I need to find A Homework Equations ∫|ψ(x)|^2 dx=1 so I know I need to evaluate it between 0 and 2/k The Attempt at a Solution My problem is do I square the whole ψ(x)? If some one could point me in right direction I...

Homework Statement What is the minimum number of points a sample space must contain in order that there exists n independent events A_1, ..., A_n , none of which has probability zero or one? Homework Equations None at this time The Attempt at a Solution I was thinking that if each A_i...

Homework Statement Prove that if you have 3 linearly independent equations in 3 variables, then there exists only 1 solution to the system. Homework Equations linear independence implies none of the equations can be expressed as a linear combination of the other equations. The...

Hi, I am using the central difference method to solve a diffusion-based partial differential equation. However, my code now will not run because the time step has to be so large that Matlab cannot handle it. The large time step is due to the stability of stability: Diffusion...

Homework Statement This isn't actually a homework question, I'm reviewing for a midterm I have coming up this week and came across this question in some of the practice exercises that were provided. Let A,B,C be three events. Suppose that A and B are independent, B and C are mutually...

As the title suggests I am working on some general relativity and combinatorics seems to be my ever-returning Achilles heel. I have a four dimensional tensor, denoted by g_abcd with a,b,c,d ranging between 0 and 3, which is fully antisymmetric, i.e.: it is zero if any of the two (or more)...

Homework Statement If a question states event A and B are "not" independent, does it mean that they are Mutually Exclusive? My brain is having hard time accepting that if they are not dependent, then they don't neccesarily have to be 'dependent'. Kinda like if its not hot, then its cold. it...

Homework Statement Toss a pair of fair dice, one in red and the other is blue. Define the events A={Red dice showing 1 or 2 or 3} B={Red dice showing 3 or 4 or 5} C={The sum of points on the two dice equals 9} Are the 3 events pairwise independent? mutually independent? Justify your answer...

If the Lagrangian is Hermitian, then fields and their complex conjugates are not independent. That is, you can solve the EOM for one field, and if you take the complex conjugate of that field, then that's how the complex conjugate field evolves: you don't have to solve the Euler-Lagrange...

Homework Statement https://www.edx.org/static/content-mit-6002x/images/circuits/H1P2.79e52b492b94.png Homework Equations It's been a while since I've done KCL/KVL, could be that I'm being just being stupid. I'm trying to find v1, i4, and the power in all the circuit elements...

Hey guys, I have a quick question. Suppose X is a chi squared random variable with n degrees of freedom and Y is another independent chi squared random variable with n degrees of freedom. Is X/Y ~ 1 ? Intuitively, it makes sense to me but I'm not too sure.

I had kind of a general question. Say I have a second order, homogeneous ODE. Say I use one of the general techniques to generate a complementary solution for my ODE and I end up with something of the form y = C1(solution1) + C2(solution2) Am I gauranteed that these two solutions will be...

U is the universal rest frame. A and B space ships pass U at t=0, moving at v. Both experience equal length contraction in the x direction. If length contraction is a result of em deformation in response to acceleration, then length expansion should be the response to deceleration. If the B...

Homework Statement Suppose that T:W -> W is a linear transformation such that Tm+1 = 0 but Tm ≠ 0. Suppose that {w1, ... , wp} is basis for Tm(W) and Tm(uk) = wk, for 1 ≤ k ≤ p. Prove that {Ti(uk) : 0 ≤ i ≤ m, 1 ≤ j ≤ p} is a linearly independent set.Homework Equations The Attempt at a Solution...

Hello everyone, this nxn matrix arises in my numerical scheme for solving a diffusion PDE. M = \left(\begin{array}{cccccccccc}1-\frac{Dk}{Vh} & \frac{Dk}{Vh} & 0 & 0 & & & \ldots & & & 0 \\[6pt] \frac{Dk}{h^2} & 1-2\frac{Dk}{h^2} & \frac{Dk}{h^2} & 0 & & & & & & \\[6pt]0 &...

Another thread in this section (https://www.physicsforums.com/showthread.php?t=619945) raises some interesting questions. I can't figure what the original poster there is asking, so I think it best to put what I'm asking in a new thread. A simple "field test" of a system that detects a...

The numbers are subscripts. U1 + U2 + U3 = V1 + V2 + V3 U1 + U2 = V2 I have tried solving for each V in terms of U, but this isn't working out too well.

Can anybody elaborate on the insulating fluid, or point me to a good source which can? This is why I ask: First, we must remember that the Earth is rotating at about 1,666 km/h about its axis. Second, the Earth is orbiting the sun at about 107,000 km/h. The sun is moving through...

Hello, I am a senior in high school as of Fall 2012 and I am new to PF. Currently I'm self studying physics in preparation for the AP exam( I am aiming for C Mech, if i am prepared in time)and am taking calculus BC. My goal is to take up a project over the summer in which i could apply...

Homework Statement Let's say the independent variable (in statistical terms) A depends on variables B, C and D. We perform tests, and find out that the variable A causes "something" with the values of B, C and D equal to B2, C2 and D2. Let's also say that A with variables B, C and D of B1...

I'm a high school student and I recently thought of a really cool study on behavior towards people dressed in different clothes - there's a little more to it than that but I don't know if you need that for this question. Anyway since I'm in high school I've never researched or done a project...

If there is a 5 percent chance of getting a particular result, and there are 15 of these events taking place simultaneously with the exact same probability, then collectively, what is the chance that one of these events will take place? For example, if 15 cars of the same make and model...

Hi there! A Hilbert space E is spanned by a set S if E is generated by the element of S. It is well known that in the finite dimensional case that S spans E and S is linearly independent set iff the set S form a basis for E. The question is that true for the infinite dimensional...

For some non-linear 3D function, let's say I want to take the partial derivative for x where y is constant. Each point for Z will be different of course since it's non-linear. So let's say I plug in an X of 3 where Y is constant for some function and I get a slope of 5 as my answer. Is it...

Homework Statement The probability of a student losing his library card is X each time he goes to the library. He goes to a different library 5 times a week, starting from Monday and ending on Friday. 1)At the end of the day on Thursday, he finally checks his wallet and realizes his library...

For the last step in the derivation of the Gross-Pitaevskii equation, we have the following equation 0=\int \eta^*(gNh\phi+gN^2\phi^*\phi^2-N\mu\phi)\ dV+\int (N\phi^*h+gN^2(\phi^2)^*\phi-N\mu\phi^*)\eta\ dV, where \eta is an arbitrary function, g,N,\mu are constants, h is the hamiltonian for...

I remember a long time ago I read or watched something that talked about a guy that had a three story antenna and he was using a tesla based circuit to draw enough electrical power to power his household- for free. I recently ran across this [crackpot link deleted] nowwww, I also ran across...

Hi guys, I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent? Thank you

Hi everyone, I was watching an MIT OpenCourseWare video where the lecturer describes the problem of a rulers motion on a frictionless surface after being subjected to a 'short' impulse orthogonal to the long axis of the ruler. (sorry as a new user I can't post images, youtube 'MIT torque...

Hi I am trying to do this problem. Verify that \( y_1=x^3 \) and \(y_2=|x|^3 \) are linearly independent solutions of the diff. equation \( x^2y''-4xy'+6y=0\) on the interval \((-\infty,\infty) \). Show that \( W(y_1,y_2)=0 \) for every real number x. I could actually show the above by...

Hey everybody! I will be attending Notre Dame this following fall, and I am hoping to major in physics, as well as research (I haven't really decided what I will to focus on, esp. at the graduate level, but I hope I can figure that out later on down the road). Over the summer, I want to...

Supposing X, Y and Z are three mutually independent continuous random variable, is multiplication X*Y and X*Z still independent? If yes, please prove it; if no, please come up with a counterexample. Thanks a lot!