Independent Definition and 713 Threads

Question: If X and Y are independent poisson variates with mean λ1 and λ2 respectively, what is the probability that i) X + Y =k ii) X = Y Solution: Dont know how to solve this .

1. (a) If ^H_1 is a small perturbation to the Hamiltonian ˆH0, show that the first order correction to the ground state (gs) energy is: ∆E = ∫ψ*_0(x)ˆH1 ψ_0(x) dx between negative and positive infinity. where ψ0(x) is the gs wavefunction of the unperturbed system. B) (b) Take...

Let Xi, i=1,...,10, be independent random variables, each uniformly distributed over (0, 1). Calculate an approximation to P(\sumXi > 6) Solution E(x) = 1/2 and Var(X) = 1/12 [How should is calulate the approxmiate ]

Question : An infinite sequence of independent trails is to be performed . Each trails resulting in a success with probability p and failure with probability 1-p . What is the probability that i) atleast 1 success occurs in the first n trails ; ii) exactly k success occur in the first n...

Homework Statement when complex integral is independent of path? i heard that its for every function f(z) but when i have function f(z)=\left(x^2+y\right)+i\left(xy\right) its not independent, why?

Homework Statement integral: \int\limits_C\cos\frac{z}{2}\mbox{d}z where C is any curve from 0 to \pi+2i The Attempt at a Solution can i do this like in real analysis when counting work between two points, just count this integral and put given data in?

Hi everyone, here's a probability problem that seems really counter-intuitive to me: Find four random variables taking values in {-1, 1} such that any three are independent but all four are not. Hint: consider products of independent random variables. My thoughts: From a set perspective...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Suppose we have time-dependent operator a(t) with the equal-time commutator [a(t),a^{\dag}(t)]=1 and in particular [a(0),a^{\dag}(0)]=1 with Hamiltonian H=\hbar \omega(a^\dag a+1/2) The Heisenberg equation of motion \frac{da}{dt}=\frac{i}{\hbar}[H,a]=-i\omega a implies...

hello :) i have a silly question and i keep confusing myself, hope someone can help me. my friend has two diseases and I want to calculate a number to represent the chance of success (i.e. him surviving both diseases for more than 5 years) disease A: chance of survival for more than 5...

Problem : Show that if event A is completely independent of Event B and C then A is independent of BUC?

http://nextbigfuture.com/2010/12/blacklight-power-announces-independient.html Can any physics buffs here make heads or tails of this? I really don't know what to think about this technology anymore :confused:...

Many textbooks make the statement that it's found experimentally that the electric force by a stationary charge on on a moving charge is independent of its velocity. Has this lead to any confusion for people here? Embarrassingly, I was using this to mean that in the proper frame of the...

I was talking to some friends last night and became interested in the topic of independent(ei. non-government or university affiliated) research institutes. While these sorts of things have typically been ruled out because of monetary concerns with the rapid advancement of cheap computing and...

Let t€R be fixed. Show that {u,v}CR^2 with u=(cost,sint), v=(-sint,cost) is a linearly inpedendent set.

Homework Statement Hello, I just want to know if I am going about this the right way. A and B are outcomes of a random experiment in a sample space \Omega such that \Omega = A\cupB. P(A) = 0.8 and P(B) = 0.5 Study if A and B, A and B^{c}, A^{c} and B, and A^{c} and B^{c} are independent...

Homework Statement Suppose that a matrix A has real entries (which we always assume) and a complex (non-real) eigenvalue  \lambda= a + ib, with  b not equal to 0. Let W = U + iV be the corresponding complex eigenvector, having real and imaginary parts U and V , respectively. Show that U...

Let x_1, x_2, ..., x_n be identically distributed independent random variables, taking values in (1, 2). If y = x_1/(x_1 + ... + x_n), then what is the expectation of y?

I've got a pretty good answer to this one already, yet I'd like to see how solid it is. I'll list the question first in quotes. Here's my work below. I credit http://arxiv.org/PS_cache/arxiv/pdf/0909/0909.1685v4.pdf" for the answer. X and Y are independent if and only if...

Homework Statement Show that every m×n matrix A with m linearly independent rows can be obtained from n × n matrix by deleting the last n − m rows. Homework Equations The Attempt at a Solution I have no idea of this question

Is it possible? Most of the resources I find are geared toward college class situations. I do not want to learn how to learn with a lecturer. Is there anything online free that can teach and quiz without acting as a supplement for an expensive course or school setting?

Homework Statement Let f:V\rightarrow V be a linear map and let v\inV be such that f^n(v)\neq0 and f^(n+1)(v)=0. Show that v,f(v),...,f^(n-1)(v) are linearly independent. The Attempt at a Solution I'm really stuck with this one. I know the definition of linear independence and...

Homework Statement Let T be a linear transformation of a vector space V into itself. Suppose x ε V is such that Tm(x)=0, Tm-1(x) not equal 0 for some positive integer m. show that x, T(x), …, Tm-1(x) are linearly independent. In regards to Tm and Tm-1 m and m-1 are upperscript on the...

Homework Statement if X and Y are independent random variables does it imply that X^2 and Y^2 are also independent? Homework Equations The Attempt at a Solution

An industrial hoist is being used in an emergency job where the weight exceeds the design limits of two of its components. For the amount of weight being lifted, the probability that the upper attachment hook will fail is 0.20. The probability that the lower hook will fail is 0.10. What is the...

Homework Statement y'' +(y')^2 = 6(y') -9 Homework Equations u = y' u' = y'' The Attempt at a Solution equation from 1 becomes u' + U^2 = 6u - 9 du/dx + u ^2 = 6u-9 du/dx = -u^2 + 6u -9 du/dx = -(u^2 +6u - 9) du/dx = -(u-3)^2 du/(u-3)^2 = - dx integrate...

Show this set of functions is linearly independent (e^(-x), x, and e^(2x)) Homework Statement f_{1}(x) = e^{-x}, f_{2}(x) = x, f_{3}(x) = e^{2x} Homework Equations Theorems and lemmas, which state that if vectors are in echelon form, they are linearly independent, and also that they are...

Hello, everyone I am studying Srednicki's "Quantum Field Theory", section 4 "The spin-statistics Theorem". Does anyone know how to show that "The time ordering of two spacetime points x and x' is frame independent if their separation is timelike."(P32), explicitly? And "Two spacetime points...

Hi, This has been bothering me for a while now.. The scalar wave equation is a 2nd order differential equation. So we would expect two independent solutions for it. However when you try to find the solution of the scalar wave equation (in spherical coordinates) by employing the separation...

Hi, I came across a question where I needed to prove that a set of vectors are linearly independent. The thing is, I am not sure how to reason the proof properly. Say you have three vectors x1,x2,x3 E R3, and prove that they are linearly independent. Put them into a 3x3 matrix A...

Hi, I have a question about counting (how difficult should that be ;) ) I have the set of tensors in D dimensions \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\} with the relations H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho} T^{\mu}t_{\mu} = 1...

Hi all, I have learned that the hydrodynamic entrance length of a channel (to form fully developed laminar flow) is correlated to the Reynolds number, because the shear effects have to propagate inwards from the walls of the channel. However recently I found out that there is a 'minimum' to the...

Ok. Sooo. Let's say u have y=x+5. Then u know y-5=x. Now if u have y=x^2 - x. How would u rearrange it to find out what x equals. I found out that in general I cannot rearrange ewquatioms with mitiplr x variables with different exponents. So help me please

Homework Statement if v_1,v_2,...,v_k be k linear independent vector, and if v_1,v_2,...v_k,v be k+1 linear dependent vector, then v is the linear combination of v_1,v_2,...,v_k Homework Equations n/a The Attempt at a Solution some of my attempt,(direct proof) v_1,v_2,...v_k,v be k+1...

Homework Statement If v11,...,vk,v are linear independent, prove that v\notin \left\langlev1,...,vk\right\rangle Homework Equations n/a The Attempt at a Solution i can prove it by contrapositive, but I'm curious how to proof it with "If v11,...,vk,v are linear...

A quote from the book of T.L. Chow 'Mathematical methods for physicists' The reader may notice that dy/dx has been treated as if it were a ratio of dy and dx, that can be manipulated independently. Mathematicians may be unhappy about this treatment. But, if necessary, we can justify it by...

Homework Statement Let \Omega=\{HH,HT,TH,TT\} and let F and U be two partitions of \Omega: F=\{G,K\} with G=\{HH,TT\} and K= \Omega\backslash G, while U=\{V,W\} where V=\{HH,TH\} and W= \Omega\backslash V. If 2^\Omega is the \sigma-algebra of \Omega, and A=2^F and B=2^U...

Should be simple, but can't figure out :) Why is that , for a field K, the linear independence of field homomorphisms g1, ..., gn: K -> K equivalent to the existence of elements a1, ..., an \in K such that the determinant det| gi(aj)| != 0 (...so, just like in a case of linear...

du/dt = d2u/dx2 u(x,t) = (t^a) * (g(e)) where e = x/sqrt(t) and a is a constant Show that integral from -inf to inf [ u(x,t) ] dx = integral from -inf to inf [ (t^a) * g(e) ] dx is independent of t only if a=-0.5 My attempt was to diff both sides by t (sorry not x) giving integral from...

Hi, Is this differential equation valid for time independent acceleration" a = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?

I understand the Michelson–Morley experiment and its result; but what I don't know yet is the REASON. Example: A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME? According...

thanks everyone I found an answer

Hey, I go to the University of Rochester, and I am currently entering my sophomore year as a physics major. Speaking to one of the physics department's staff members at the school, I was able to set up a research position with one of the professors in the astrophysics department. In order for...

Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...

Hi All I was re-reading the first pages of the book from Mr Claude Cohen-Tannoudji ,... (Quantum Mechanics) and something called my attention. In commenting the appearence , in 1905, of the photon notion in Albert Einstein's paper on photelectric effect, he (Mr. Claude) says that only in...

Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim

I've looked it up and can't really find a clear answer.. For a system of 3 simultaneous linear equations, is there any difference between 'the equations are linearly independent' and 'the equations have a unique solution'. If so what is it? Thanks!

Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...

For (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) let Xk = [∑(from i=1 to k) Yi] / [∑(from i=1 to k+1) Yi] where k = 1,2,3 How can I prove X = (X1, X2, X3) is independent? What I did was... (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) = (Z1, Z2, Z3, Z4) / (Z1+Z2+Z3+Z4+Z5) where Z ~ N(0,1), Z IID G(1/2) Now...

I still can't visualise them. They deliver the same current all the time, however there is no potential drop across them. Is it just a theoretical device that doesn't exit? I am sure current sources do not add new charge into the circuit, but rather move charges around but this requires a...