Independent Definition and 713 Threads

After time t, the probability of monochromatic absorption of the ground state |1> to the energy state |n> is given by: |<n|1>|^2=4|U_{n1}|^2\frac{\sin^2((E_n-E_1-\hbar\omega)t/2\hbar)}{(E_n-E_1-\hbar\omega)^2} where U is the transition matrix. The claim is that as t goes to infinity, the...

Why column 1 is M^2*v? How can we know? Please see attached. Many thanks.

Homework Statement Check if the following set of vectors are linearly dependent or independent: A) V1= \stackrel{1}{1} V2= \stackrel{1}{3} B) V1= \stackrel{\stackrel{1}{2}}{3} V2= \stackrel{\stackrel{2}{1}}{3} C) V1= \stackrel{1}{3} V2= \stackrel{2}{1} V3= \stackrel{-1}{2} Homework...

Please see attached question. I can finish part (a) For part b, how can I find ø(v) ? Although I can find ø(v1) and ø(v2) but I think it is unrelated to ø(v)...

Please see attached question. I can finish part (a) For part b, how can I find ø(v) ? Although I can find ø(v1) and ø(v2) but I think it is unrelated to ø(v)...

Hi, I am a Junior in high school and if I can, I would like to do Independent Study next year based on either the OCW for http://ocw.mit.edu/courses/physics/8-20-introduction-to-special-relativity-january-iap-2005/ or 8.033 - Relativity. I wanted to know if they most likely would be possible for...

I know eigenvectors corresponding to different eigenvalues are linearly independent but what about a set ${e_{1},...,e_{n}}$ of eigenvectors corresponding to different eigenvalues?

Homework Statement As the title indicates. I'm given two independent exponential distributions with means of 10 and 20. I need to calculate the probability that the sum of a point from each of the distributions is greater than 30. Homework Equations X is Exp(10) Y is Exp(20) f(x) =...

Hi, i was wondering if the following is valid: E[x/y] = E[x] / E[y], given that {x,y} are non-negative and independent random variables and E[.] stands for the expectation operator. Thanks

Hello, I have a question with regards to solving problems that require knowledge of which variable is dependent and which is independent. Suppose I am presented with the differential equation x^5 y^{(4)} - x^3 y'' + 6y = 0; for this differential equation I am asked to determine if it is linear...

Hi, This is not a homework question. I need to calculate input impedance for a LNA and this is part of it. How do you calculate input impedance, Zin, for the circuit below? I tried by applying an input voltage, V1, and calculate Iin. Input impedance will be V1/Iin. However, the expression...

Hi, http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf (see page 8, sum of two independent random variables). I don't understand why they had to go further into the limits, 1 < z < 2. Why do they have to do that? And also, where did they get it...

Suppose I have two atoms that independently emit alpha particles. I want to find the mean \Delta T for the events. I then want to extend this for 3, 4 etc. atoms however what I'd like to do for more than 3 atoms is find the smallest delta T for any two emissions. What should I look at to...

http://postimg.org/image/8jqk9q6rp/ Can someone explain what "independent system displacement variables" are? http://postimg.org/image/eypl6edhh/ What are the independent system displacement variables in this diagram? thanks

I am solving a question that asks me to find an H field in phasor form from the given E field in phasor form Es = j30(beta)(I)(dl)sin(theta)e^(-j(beta)r) a(theta) V/m Given that the EM wave propagates in free space. Why do I get different answers if I : 1) Divide Es by the magnitude...

1. Prove that if A is symmetric and B is skew-symmetric, then {A,B} is a linearly independent set. I am going to need some help to solve this. Not sure how to begin. Homework Equations The Attempt at a Solution

I am conducting a lab in my class and was wondering, which is the dependant and independent variable and also which one goes on the y or x axis. It is a net force vs acceleration. I am thinking that net force is the independent variable.

Hi, i would like to have a hint for the following problem: Let $$v_1, v_2 \&\ v_3 $$ in a vector space V over a field F such that$$ v_1+v_2+v_3=0$$, Show that $\{v_1,v_2\}$ spans the same subspace as $\{v_2,v_3\}$ Thanks in advance

Graph Theory -- Max. Independent set algorithm Homework Statement Design a polynomial time greedy algorithm to compute a maximum independent set for a graph. Explain the algorithm and compute T_w(n). Homework Equations The Attempt at a Solution My terse and informal...

Homework Statement For the forced damped oscillator, show that the following are frequency independent. a) displacement amplitude at low frequencies. b) the velocity amplitude at velocity resonance. c) the acceleration amplitude at very high frequencies Homework Equations...

Is the title statement true? Was doing some studying today and this caught my eye, haven't looked into linear algebra in quite a while so I'm not sure how it is true :/ Internet couldn't provide any decisive conclusions neither Many thanks

Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.

Hello, How am I to find then number of independent equations in a set using matrix techniques? Thanks

Homework Statement Three yearly losses. First: Exponential Second & Third: Weibull Losses are independent. Find the 95% VaR of the min loss Homework Equations The Attempt at a Solution My first thought was: Let L be total loss, A be first Loss, B be second loss, C be third...

My professor asked me to provide a circuit design for a voltage divider biasing circuit whereby the transistor beta is independent of the voltage gain, which he wants to be -100. I maintain this is impossible, as Ic = B*Ib, changing the beta obviously effects the gain. Right? (not...

Hi there. I have to find the energy corrections through the perturbation method, and then give the exact result for the hamiltonian: ##H= \begin{pmatrix} E_A & \epsilon & \epsilon & \epsilon \\ \epsilon & E_B & 0 & 0 \\ \epsilon & 0 & E_B & 0\\ \epsilon & 0 & 0 & E_B \\ \end{pmatrix} ## So...

Hello, I am currently in high school and I recently got the opportunity to do an independent study with one of my teachers and I am struggling to come up with what to study. I have taken calculus 1, 2, and 3, differential equations (with a bit of linear algebra), and calculus-based mechanics and...

I've often read that the emission spectrum of a fluorescent molecule is independent of the wavelength used for the excitation. But what happens in the case of a small Stoke's shift where the excitation and emission wavelengths overlap? If I use a narrow band excitation with a wavelength in...

Provided I know that after 10 attempts I will get 8 successes with a probability of a success per try being 'p', does that affect the success of the first try? My first instinct was to say it's independent because each attempt is independent but now I know this is a special case where "I know...

If A and B are two independent events then P(A intersection B) = P(A).P(B) I don't refute this but it confuses me. What is the sample space in this? For eg: - If A is the event that we get Head while tossing a coin and B is the event that we get 2 while throwing a die, then what will we be the...

So at my gym, there's a cable machine that works like this: You pull on one cable and you lift x mass using y force. You pull the other and find the same thing. If, however, you pull on both, you're still only lifting x mass (you can see the weights) yet somehow each cable is still requiring y...

Are they always independent from each other so that you can multiply their E[X] together to form another E[X] with the same distribution and pmf or pdf?

Homework Statement Let a1, a2, ... an be vectors in Rn and assume that they are mutually perpendicular and none of them equals 0. Prove that they are linearly independent. Homework Equations The Attempt at a Solution Consider βiai + βjaj ≠ 0 for all i, j => βiai + βjaj +...

Two independent events have probabilities 0.1 and 0.3. What is the probability that at least one of the events occurs? I have an answer of .37, when I looked up the solution it is the same value but it was solved another way. I was just wondering if my logic would work. Find $P(a \cup b) =...

Hello all, I have been given a problem where I am asked to calculate "all" the components of the Riemann tensor in a gross non-diagonalized metric. I know there exists at most 20 independent components of Riemann, but I want to actually compose a list of these combinations. It is easy...

hello! I'm trying to understand the following property: Let X and Y be independent random variables z: = X + Y. Then http://imageshack.us/a/img268/9228/71pe.png where fZ (z) is the probability mass function for a discrete random variable defined as follows...

1. The problem: A 5-kg block is moved from the ground to a height of 1 m via two different routes, vertically and along an inclined plane with angle of 30° to the horizontal. How much work is done on the block against gravity in each case? Homework Equations W=Fcosθd where θ is between...

I'm having trouble figuring out how a field and it's conjugate are independent quantities. How can they be, when they are related by conjugation? Suppose you have real fields x and y, and form fields: L=(x+iy)/sqrt2 R=(x-iy)/sqrt2 In a path integral, you'd have .5(∂x∂x+∂y∂y) in your...

Homework Statement Prove the following theorum: The time-independent wave function ## \psi (x) ## can always be taken to be real (unlike ##\Psi (x,t) ##, which is necessarily complex). This doesn't mean that every solution to the time independent Schrodinger equation is real; what it says is...

Something is throwing me here. No matter how fast one is going, relatively speaking, one is in the same universe as everyone (and everything) else. We're all going through the same spacetime, albeit at different velocities. You're in the same universe as I am and we both see the same space...

Hi there, I have a homework where I have to do this: Prove that square matrix is invertible if the columns of the matrix are linearly independent. There is also a hint: You can help with the following statement: Linear transformation L: U->V is bijection when a vector space basis N for U...

Homework Statement There is a vector space with real entries of all 2x2 matrices. You have to find what values of \alpha\inℝ make the set Z = \{ \begin{pmatrix} 1 & 2\\ 1 & 0 \end{pmatrix}, \begin{pmatrix} 3 & 7\\ 0 & 0 \end{pmatrix}, \begin{pmatrix} 2 & 6\\ \alpha & 0...

Hello! I, like many others, am interested in studying physics on my own as my school doesn't offer any kind of physics for ninth graders. (The tenth grade physics class isn't very in depth either; I took part of it in 8th grade). I have exhausted what Khan Academy has to offer, and I am...

Hello, I'm hoping I might be able to get some help in creating a forecasting model (in sports) looking at 2 variables that are not independent of each other. I'll take US Football (same applies to rugby) as an example. The specific forecast I'm interested in here is the expected supremacy...

Hello! I was reading this excellent article about position independent code and it's implementation for shared libraries. I'm still confused about one part though. My current understanding is that the offset between the code section and data section is known at compile time. Since this offset...

Homework Statement Determine whether the following vectors are linearly independent in P3 "not sure what P3 stands for maybe polynomial of third degree?" 1,x2,x2-2 let p1(x)=1 p2(X)=x2 p3=x2-2 c1p1(x)+c2p2(x)+c3p3(x)=z where z=0x2+0x+0 I then create a matrix using the above...

I just had a question pertaining a circuit that consists of 3 loops in the attached picture: The textbook states that the loop inside with the 50[V] source is independent of the rest of the circuit, but I have a hard time rationalizing it. The only reason I feel it is the case is because the...

Is it possible to derive ideas of angular momentum form linear momentum. Can linear momentum and calculus be used to derive ideas of angular momentum.

I met with a REALLY nice professor who is doing theoretical nuclear and particle physics (one of my interests). I am in my first year, but can graduate in three years instead of four because of AP credit (with already having taken AP Physics with Calculus and am currently taking Quantum). So he...

Given that the joint probability Pr(w,x,y,z) over four variables factorizes as Pr(w,x,y,z) = Pr(w) Pr(z|y) Pr(y|x,w)Pr(x) show that x is independent of w by showing that Pr(x,w) = Pr(x)Pr(w). Attempt: if we simply assume Pr(x,w) = Pr(x)Pr(w), then: \begin{align} Pr(w,x,y,z) &= Pr(w)...