Independent Definition and 713 Threads

Homework Statement 2. Let a random experiment be the cast one “six-sided” die and one “four-sided” die. (a) Give an example of two independent events and justify your answer. (b) Give an example of two dependent events from this sample space and justify your answer. Homework Equations...

I'm currently taking a Semiconductor class and we're talking about Schrodinger's Wave Equation, specifically the 1 dimensional time independent form. We were looking at the infinite potential well model: And we divided the graph into 3 different regions: first being the left (or...

A formula I know for the number of functionally independent components of the curvature tensor is: (n^2)(n^2 -1)/12. It gives 1 for n=2, 6 for n=2, 20 for n=4. However, for a metric space (with symmetric metric), the curvature tensor is completely specified by the metric tensor. For n=4...

Which of the following is more likely to be generated using independent random flips? Explain. Pls help! Thanks!

What will happen to the following circuits immediately after T is closed? Obs: A) 2 generators of voltage 3V and V, 2 resistors of resistance R and 2R B) 2 generators of voltage 3V and V (second inverted), 2 resistors of resistance R and 2R C) 1 generator of voltage 3V, 1 capacitor...

Maxwell equations are 8. we need them to determine electric and magnetic field. the component of magnetic and electric field are 6. in linear algebra say for solving a system of equation with n free variable, we need n equations to solving it uniquely. here arises a question and that...

Homework Statement Let B = 1 0 6 -1 Be a square matrix. Find a non-singular matrix P such that P-1BP = D, where D is a diagonal matrix and show that P-1BP = D. Homework Equations det(lambdaI - A) = 0 The Attempt at a Solution Ok, this might look like a simple...

Homework Statement Let X and Y be independent random variables. Prove that g(X) and h(Y) are also independent where g and h are functions. Homework Equations I did some research and somehow stumbled upon how E(XY) = E(X)E(Y) is important in the proof. f(x,y) = f(x)f(y) F(x,y) =...

Hello, I need to solve numerically an equation of the form v(t) = k1*z(t)*w(t)-k2*i(t)-k3*di(t)/dt The issue is that rungekutta methods are useful for solving di(t)/dt = 1/k3 * [ k1*z(t)*w(t)-k2*i(t)-k3*-v(t) ] but I need to solve for v(t) What I did was: v...

I have the chance to do an independent study on CS this semester, and I'm here for suggestions. Since it's only high school, and the teacher has no CS knowledge, I can get away with studying anything from learning a library and making a small project with it to working on my hobby kernel. The...

Homework Statement Hey everyone, I am doing youngs double slit experiment to find the wavelength of a light source but i am having a lot of trouble finding the independent and dependent variables. Can people suggest what they could be? Thanks. Also, some controlled variables would be...

so i know for example that d/dt (∂L/∂x*i) = ∂L/∂xi for cartesian coordinates, where xi is the ith coordinate in Rn and x*i is the derivative of the ith coordinate xi with respect to time. L represents the lagrangian. so using an arbitrary change of coordinates, qi = qi(x1, x2, ..., xn) i...

Do you think Independents are the more mature choice? I mean I don't know of an 18 year old who is independent. Or doubt there are many young people in the Independent camp. Further, they don't seem to be clouded by any closed ideas or principles nor too open to overwhelming change. They seem...

Given matrices in a vectorspace, how do you go about determining if they are independent or not? Since elements in a given vectorspace (like matrices) are vector elements of the space, I think we'd solve this the same way as we've solved for vectors in R1 -- c1u1 + c2u2 + c3u3 = 0. But I'm...

In treating the complex scalar field in QFT, \phi and \phi^\dagger are treated as independent variables. I'd like to make sure I understand what this actually means: Is this the same idea as treating \phi and \partial \phi as independent variables in the Lagrangian? Formally, we view the...

In an ANOVA experiment, you have, group mean \overline{y}. overall mean \overline{y}.. Are they independent? Some samples overlap to calculate these means. What is var(\overline{y}.-\overline{y}..) ?

Hi, I'm an independent game developer (currently in college) and have been trying to solve a problem and get an equation for use within my physics engine. Homework Statement Here's the problem/situation illustrated through two graphs and a diagram: http://i.imgur.com/qHAsU.jpg Homework...

I'm working on a gravity simulator and I can't help but feel that I've done something wrong. Extremely large bodies take a longer time to fall into each other than smaller ones. Is this right? Like for example, if you had to bodies of solar mass at 1 AU apart, would it take a longer, shorter or...

What is the difference between disjoint and independent events, how will the 2 affect calculations involving them?

hey i have the set s = {(t,1,1),(1,t,1),(1,1,t)} and i want to find for which values of t this set is linearly independent. For a set of vectors containing all numbers i setup c1v1 + c2v2 .. +cnvn = 0 and I need the only solution to be c1=c2=c3..=cn=0 for linear independence. so then put...

Homework Statement so I'm trying to find the general solution of this problem: \mathbf {x'} = \begin{bmatrix} 2 & 0\\0 & 2\end{bmatrix}\mathbf{x} Homework Equations det(A- rI) = 0 The Attempt at a Solution det(A - rI) = det \begin{bmatrix} 2-r & 0 \\ 0 & 2-r \end{bmatrix} =...

can someone explain physically why escape velocity is independent of angle of projection.

Hi, I have a differential equation that I just can't seem to solve. Now here's the deal: I'm sure there are advanced methods that would easily solve this equation, but the equation is in the chapter on First-Oder Linear Equations, so it shouldn't be anything fancy. There's even a hint: it...

Homework Statement Prove mathematically that the coefficient of friction is independent of the mass of a rider at a fixed location from the center on a merry go round. Homework Equations F = ma? The Attempt at a Solution I honestly don't know - I can't find two starting equations...

Independent virtual particle after "mind experiment" annihilation Hello good people, Probably a bit of a silly question, but I have been entertaining a bit of a thought experiment about the following. Consider the following: 1. A virtual photon is exchanged between two electrons to...

First there was the French province of Québec which was conquered by the British in 1763. Later came the loyalists from those rebellious colonies to the south who settled in what would become the province of Ontario. This was the beginning of Canada. In 1867 the British North America Act gave...

If I'm given a set of vectors {-4; 3; -10} = v1 {2; -2; -3+k} = v2 {2; -6; 14} = v3 I want to find that they are linearly independent if and only if k != something to solve this is simple but a huge tedious pain (although not nearly as tedious as trying to find a solution to this...

Homework Statement Show that the line integral is path independent and evaluate the integral \int_C tan(y) dx + x sec^2 (y) dy The Attempt at a Solution \frac{\partial }{\partial x}(tan(y)) = 0 \neq 2xsec^2(y)tan(y) = x\frac{\partial }{\partial y}(sec^2(y))

Homework Statement Consider independent random variables X1, X2, X3, and X4 having pdf: fx(x) = 2x over the interval (0,1) Give the pdf of the sample maximum V = max{X1,X2,X3,X4}. The Attempt at a Solution I can't find ANYTHING about how to solve this in the book, please help!

Hey guys, I was imagining that I have a sine function: y = sin(x) where x represents a distance in meters for instance. Now let us say that I sample the function at x = 0,1,2,3...,10 (meters) producing a list of values: {sin(1), sin(2), sin(3),...,sin(10)} = {0.000, 0.841, 0.909, 0.141...

Homework Statement Given a set of solutions |psi_n> to the TISE show that a) |Capital-psi>=Sum(C_n|psi_n>) is not a solution to the TISE Homework Equations ***H|psi_n>=E_n|psi_n> The Attempt at a Solution I don't really know where to start, I plugged |psi_n> into *** and I am...

Pardon my ignorance but why does the Time Independent Schrödinger equation use Time? It uses a kinetic energy operator. Kinetic energy; "It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity." Velocity is; "The scalar absolute value...

Homework Statement The random variables X1 and X2 are independent and identically distributed with common density fX(x) = e-x for x>0. Determine the distribution function for the random variable Y given by Y = X1 + X2. Homework Equations Not sure. Question is from Ch4 of the book, and...

Okay, so I have a fair amount of knowledge in mathematics, through calculus, and I want to study physics independently. I was told that I should start with classical mechanics. Is that right, and if so, where should I go from there. What are good books to learn from. I apologize if this is a...

Suppose B = {b1,...,bn} and C={c1,...,cn} both are basis set for space V. D = {d1,...,dn} is basis for space T. If B and D is linearly independent, is C and D always independent too? How can we prove (disprove) it?

does gravity effect viscosity ? is viscosity independent od gravity ?

Homework Statement I need to argue this properly Let's say I have a matrix A and rref(A) is given as \begin{bmatrix} 1 & 0&-1 \\ 0& 1 & -1 \end{bmatrix} Since I have a pivot in every row, why isn't this linearly independent? Don't give me other arguments like "because there...

Prove this function satisfies the time independent schrodinger equation. When V is constant. Psi = A e^(i k x) + B e^(-i k x) Attempt: Time independent schrodinger equation : (- (hbar^2) / 2m) * (d^2 Psi / d x^2) + V Psi = E Psi Second order derivative of Psi : (-k^2 A e^(i k x)) + (-...

Special Relativity is just a special case where spacetime is flat and fixed. Meaning it is not really a correct picture of reality because nature chooses curved spacetime that is background independent. So quantum particles shouldn't be occurring in a flat fixed background but a dynamic...

Homework Statement Here is a really simple lin.alg problem that for some reason I'm having trouble doing. Assume that \left\{ v_i \right\} is a set of linearly independent vectors. Take w to be a non-zero vector that can be written as a linear combination of the v_i . Show that \left\{ v_i...

What does it mean by "independent"(in gauge fixing of EM field) In my textbook, it gives the Coulomb gauge \phi = 0,\nabla A = 0 and says they will kill two degrees of freedom of the four potential and leave two independent components. I understand \phi = 0 will kill one degree of freedom...

Homework Statement Basically, the title says it all, I need to figure out whether these functions are linearly independtend on (-infinity, infinity) Homework Equations Wronskian (the determinant of the matrix composed of the functions in the first row, first derivative in the second...

Suppose X and Y are Uniform(-1, 1) such that X and Y are independent and identically distributed. What is the density of Z = X + Y? Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise The...

Homework Statement Well as the title describes, x and y linear independent in R^n S is a subspace in Rn spanned by x,y i.e S= span(x,y) define the matrix A as A=xy^T+yx^T This is actually a 3 part question 1 show that A is symmetrical 2 show that N(A)=S(Perpendicular) 3 show that the...

Hi Guys, I've used this forum as a great resource for a while now and it's always helped me out. Now I'm really stuck on something and was hoping you guys could help out. It's a pretty long question, but if you guys can just give me a general direction of what to do, I can go ahead and work it...

Homework Statement I need to prove that, if {u;v;w} is a linearly independent set in a vector space, then the set {2u + v + w; u + 2v + w; u + v + 2w} is also linearly independent. Homework Equations ... The Attempt at a Solution if {u;v;w} is a linearly independent set=>...

If a and 77 are relatively prime, show that for positive integers n, a^(10^n) modulo 77 is independent of n. I think I don't understand what this statement is asking. a^(10^n) modulo 77 independent of n means that a^(10^n) modulo 77 is always going to be the same or something?

How do I explain it?? Potential difference in the system discussed is independent Hi folks, - please view the attached image - my colleague and I had a major disagreement in the office. We both mutually put a lid on the discussion as we both felt that we needed more information in order to...

Homework Statement V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V. Homework Equations None that I can think of. The Attempt at a Solution So to be...

Suppose X and Y are independent Poisson random variables, each with mean 1, obtain i) P(X+Y)=4 ii)E[(X+Y)^2] I m trying to solve this problem but have difficulty starting ... If some one could give me a some pointers