What is Expectation: Definition and 688 Discussions

Expectation damages are damages recoverable from a breach of contract by the non-breaching party. An award of expectation damages protects the injured party's interest in realising the value of the expectancy that was created by the promise of the other party. Thus, the impact of the breach on the promisee is to be effectively "undone" with the award of expectation damages.The purpose of expectation damages is to put the non-breaching party in the position it would have occupied had the contract been fulfilled. Expectation damages can be contrasted to reliance damages and restitution damages, which are remedies that address other types of interests of parties involved in enforceable promises.The default for expectation damages are monetary damages which are subject to limitations or exceptions (see below)
Expectation damages are measured by the diminution in value, coupled with consequential and incidental damages.

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  1. A

    The expectation value in quantum theory

    Going from the abstract state vector lψ> and the mean-value of an observable x (operator) given by: <x> = <ψlxlψ> I want to show how that is done in the position basis: So I take: <x> = <ψlxlψ> And insert completeness in front of the state vector to get the expansion involving the...
  2. K

    Conditional Expectation of a random variable

    My professor made a rather concise statement in class, which sums to this: E(Y|X=xi) = constant. E(Y|X )= variable. Could anyone help me understand how the expectation is calculated for the second case? I understand that for different values of xi, we'll have different values for the...
  3. K

    Calculating Conditional Expectation of X,Y,Z: Triangle Inequality

    1. Let T = (X,Y,Z) be a Gaussian for which X,Y,Z for which X, Y, Z are standard normals, such that E[XY] = E[YZ] = E[XZ] = 1/2. A) Calculate the characteristics function Φ_T(u,v,w) of T. B) Calculate the density of T. 2. Let X and Y be N(0,1) (standard normals), not necessarily...
  4. J

    Expectation values of harmonic oscillator in general state

    So, this has been bothering me for a while. Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates: \Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h) Is it true in this case that <V> =(1/2) <E> . I tried calculating this but i...
  5. J

    Expectation Value of Momentum

    Good Evening Fellows, I have the following question, So far I have learned that the expectation value of momentum is equal the time derivative of the expectation value of position. If the potential only depends upon position and not on time. Then, if we use the time independent schrodinger...
  6. M

    Simple statistics expectation calculation

    Homework Statement I am just trying to figure out how to calculate the expectation of something. The context is for a random sample from a normal distribution with known mean μ and unknown variance σ2. Homework Equations 3. The solution So for the purposes of this question we set θ = σ2 I...
  7. G

    Conditional expectation of a product of two independent random variables

    Suppose that α and β are independently distributed random variables, with means; μ_α, μ_b and variances; δ_α^2, δ_β^2, respectively. Further, let c=αβ+e, where e is independently distributed from α and β with mean 0 and variance δ_e^2. Does it hold that E(αβ | c) = E(α|c)...
  8. C

    Probability with expectation and variance

    A robot arm solders a component on a motherboard. The arm has small tiny errors when locating the correct place on the board. This exercise tries to determine the magnitude of the error so that we know the physical limitations for the size of the component connections. Let us say that the...
  9. P

    Time Dependence of Expectation Values

    Hi, Please refer to this book (in google archive), and go to section 7.7 (page 85)...
  10. R

    Expectation value of z component of angular momentum for a particle on a ring

    I have to find the expectation value of the z component of the angular momentum for a particle on a ring and the expectation value of the z component of the angular momentum squared for a particle on a ring. The wavefunction is e^((± imx)) I've determined that the expectation value for the...
  11. C

    Expectation value for electron in groundstate

    Homework Statement Show that the expectation value for r for an electron in the groundstate of a one-electron-atom is: <r>=(3/2)a_{0}/Z Homework Equations Expectationvalue: <f(x)>=∫\psi*f(x)\psidx, -∞<x>∞ \psi_{100}=C_{100} exp(-Zr/a_{0}), a_{o}\ =\ 0.5291\ \times\ 10^{-10}m , h\...
  12. A

    Using uncertainty principle to find minimum Kinetic Energy expectation value

    Homework Statement Assume that a particle travels with a certain known (average) velocity ##v = \left\langle\hat{p}/m\right\rangle##. You know it's position with an uncertainty ##Δx##. Use the uncertainty principle to determine the least possible value for the article's kinetic energy...
  13. C

    Integrating the Expectation Value

    I am asked a problem where I'm supposed to integrate the expectation value of a dynamic variable (operator) to solve a differential equation. OK, is the expectation value supposed to be a variable? But it seems to me like its a definite integral over allspace and thus is a number. So...
  14. S

    Conditional Expectation

    1. Let the joint pdf be f(x,y) = 2 ; 0<x<y<1 ; 0<y<1 Find E(Y|x) and E(X|y)Homework Equations E(Y|x) = \int Y*f(y|x)dy f(y|x) = f(x,y) / f(x) The Attempt at a Solution f(x) = \int 2dy from 0 to y = 2y f(y|x) = f(x,y)/f(x) = 1/2y E(Y|x) = \int Y/2Y dy from x to 1 = \int 1/2 dy from x to 1 =...
  15. L

    Computing the expectation value of momentum, kinetic energy, and compute

    [b]1. consider this wave function ψ(x)=(√(30/L^5))(L-x) if 0≤x≤L and 0 else [b]2. Compute the expectation value of the momentum. Compute the expectation value of the kinetic energy. Compute Δ p⋅Δ x...
  16. J

    Question if expectation value is considered a measurement?

    Hello, I was just curious about expectation values. One of the postulates of quantum mechanics state: The only possible results of a measurement is an eigenvalue of the operator. Now, is the expectation value considered a measurement, thus considered an eigenvalue? Thanks!
  17. K

    Expectation Values of Angular Momentum Operators

    Homework Statement Show that < l,m | Lx2 - Ly2 | l,m > = 0 Homework Equations L2 = Lx2 + Ly2 + Lz2 [ Lx, Ly ] = i h Lz [ L, Lz ] = i h Lx [ Lz, Lx ] = i h Ly The Attempt at a Solution I tried substituting different commutation values in place of Lx and Ly, but I'm...
  18. U

    MHB Proving conditional expectation

    Hi guys, assume we have an equality involving 2 random variables U and X such that E(U|X) = E(U)=0, now I was told that this assumption implies that E(U^2|X) = E(U^2). However I'm not sure on how to prove this, if anyone could show me that'd be great!
  19. S

    Difference between eigenvalue and an expectation value

    difference between eigenvalue and an expectation value of an observable. in what circumstances may they be the same? from what i understand, an expectation value is the average value of a repeated value, it might be the same as eigen value, when the system is a pure eigenstate.. am i right?
  20. K

    Some inconsistency on operator expectation value

    Consider two Hermitian operator A, B; Define [A,B]=iC, then operator C is also Hermitian. we calculate the expectation value with respect to |a>, one eigenstate of A with the eigenvalue a. From the left side, we have: <a|[A,B]|a>=<a|(AB-BA)|a>=(a-a)<a|B|a>=0, while on the right side...
  21. S

    Expectation value of a finite well, and superposition of first two states.

    Homework Statement the first two energy eigenstates of a 1 nm wide finite well of barrier height 8vo have energy eigen values of 0.66ε and 2.6ε. calculate the expectation value of a linear superposition of these states? Homework Equations airy equations The Attempt at a Solution...
  22. S

    Calculating the expectation value for a particles energy in a 1_D well

    expectation value for a particle in a 1-D well how do i calculate the expectation value for the particles energy in a 1-D well. i have attached a word file, with my working out, just not quite sure if I am on the right track... i appreciate any help...thanks a mill
  23. Z

    Why Does cos(x)^2 Average to 1/3 Over a Sphere's Solid Angle?

    Homework Statement This question comes from calculating the Einstein A and B coefficients. I am supposed to find the average value of cos(x)^2 over the solid angle of a sphere which is 1/3. And I need to show this. A similar course in a different uni just says that For...
  24. Z

    Probability density function,normalize and expectation values

    Homework Statement The probablity density function of the n-state of an electron is proportional to fn=(\frac{rz}{a_{0}})^{2n}e^ \frac{-2Zr}{\large na_{0}} show that the expectation value of the potential energy of the electron in the n-th quantum state of the hydrogen atoms is...
  25. D

    Equality of expectation value integral over coordinate space and over energy

    Dear all, I'm wondering, how one could justify mathematically the equality \int O(E(\vec{x}_1,...\vec{x}_N)) exp(-\beta E(\vec{x}_1,...,\vec{x}_N)) d\vec{x}_1...d\vec{x}_N = \int g(E) O(E) exp(-\beta E) dE where O(E(x)) is an observable and g(E) the density of states. Is there a...
  26. N

    Is the Factorization of Product Expectation Values Valid in Steady State?

    Homework Statement Hi I have read a paper, where they want to find the average number of photons in a cavity. They have an expression for \langle{\hat a}\rangle, and then they use \langle{\hat a}\rangle^* = \langle{\hat a^\dagger}\rangle to find \langle{\hat a^\dagger \hat a}\rangle. I agree...
  27. N

    QM: Expectation value relation

    Homework Statement Hi My book uses the following in a calculation \left\langle a \right\rangle \left\langle {b^\dagger } \right\rangle + \left\langle {a^\dagger } \right\rangle \left\langle b \right\rangle = 2\operatorname{Re} \left[ {\left\langle a \right\rangle \left\langle {b^\dagger...
  28. E

    What is the Meaning of Expectation and Deviation of an Operator?

    What does the expectation and deviation of an operator mean?? The way I understood it was every observable has a operator to it and the expectation of the observable uses the operator to calculate the deviation ... for ex :: <p>=integral( (si)* momentum operator (si) ) dx ... so what does...
  29. M

    Age expectation if a person is immortal if he's not murdered

    A while back I posted a thread about the probability that someone who is alive at 12 years of age will be alive at age 82. This person could only die if he were murdered or if he died when he was greater than 82 years old. Now, let's assume this person will live forever if he's not murdered...
  30. sunrah

    Expectation value via trace

    Homework Statement given \mid \psi \rangle = \frac{1}{\sqrt{2}} (\mid1\rangle + \mid2\rangle ) where \mid1\rangle, \mid2\rangle are orthonormal calculate i)density operator ii) \langle A \rangle where A is an observable Homework Equations The Attempt at a Solution i) \rho = \frac{1}{2}...
  31. B

    Commutators and Expectation Values

    Homework Statement Here's a link to an image of the exam question. It appears in the exam every couple of years, and it's due in my exam this coming week. I've looked in both the textbook and the course notes, and they simply *state* the conclusion, so I don't have a way of proving it, and...
  32. A

    Expectation value for CDF fails

    Hi, (Sorry for the slight misnomer in the title... I can't edit it!) I'm doing several problems to compute the expectation value and variances of sub-samples & operations on the normal distribution; and I am having trouble getting results that agree with numerical simulations. I have several...
  33. H

    Simple Expectation Value Question

    I was told that given a probability distribution p(x) dx, the expected value for x is given by: <x> = Ʃ xi P(xi) = ∫ x P(x) dx This part makes sense to me. It was justified to me through the use of weighted averages. However, my teacher then made a hand-wavy move to generalize the above...
  34. J

    Expectation of a product of Brownian Motions

    Let Bt1, Bt2 and Bt3 be standard Brownian motions with ~N(0,1). Then what is E[Bt1.Bt2.Bt3] ? Any help would be much appreciated.
  35. K

    Expectation Value for system of identical particles

    Dear All: I have a quite mysterious and cumbersome question concerning with the expectation values for a system of identical particles. For example, suppose I have a system of N identical bosons given by the wavefunction ψ(x1,x2,...xN), which is of course symmetrized. My concern is: 1...
  36. S

    Difference between an expectation value and an average

    Hi everyone, What is the difference between an expectation value and an average. I may have this wrong, but is it something along these lines: You perform a series of measurements on a given observable, such as momentum, and the average value of all these measurements is your expectation...
  37. M

    Simplifying Expectations of Dependent Variables

    Homework Statement if x1 and x2 are dependent, and y1 and y2 are dependent, but all the x are independent of all the y. Then how can one simplify E(x1y1x2y2)? the textbook says E(x1x2)E(y1y2) So is the rule that you can not just separate two independent variables which they are...
  38. M

    Probability - Conditional Expectation

    My professor explained this concept absolutely horribly and I have no idea how to do these problems. Let A and B be independent Poisson random variables with parameters α and β, respectively. Find the conditional expectation of A given A + B = c. (Hint: For discrete random variables, there...
  39. I

    Probability: Conditional expectation

    Homework Statement What is the expected number of flips of a biased coin with probability of heads 'p', until two consecutive flips are heads?Homework Equations The Attempt at a Solution Let T_1 = first flip is tails, H_1 = first flip is heads. and T_2, H_2 for second flip. \mathbb{E}[X] =...
  40. E

    Expectation value calculation

    How can we compute the expectation value, <\widehat{x}\widehat{p}> where ψ(x) is a normalized wavefunction? (The result is i\hbar/2)
  41. J

    To find the expectation value of momentum

    Homework Statement At time t=0 a particle is described by a one dimensional wavefunction (capital)ψ(x,0)= (2a/)^(1/4) e^(-ikx)e^(-ax^2) (three lines)=(2a/)^(1/4) e^(-ikx-ax^2)--------equation 1 k and a are real positive constants Homework Equations I think this is the one <p subscript(x)> =...
  42. F

    MATLAB What is the Expectation Value of (X'*X)^-1 in MATLAB for Signal Constellations?

    Hi, as I am new in Matlab, so I need your help. I want to replace the following inverse matrix (X'*X)^-1 with its expectation value: E{(X'*X)^-1} = E{|1/Xk|^2}I X'*X and (X'*X)^-1 is a diagonal matrix. Could anyone give me an Idea how to write it in MATLAB this expectation value...
  43. L

    Expectation value of Normal ordered Stress-energy tensor

    Hi, In Birrel and Davies ch4 they write: \langle \psi|:T_{ab}:|\psi \rangle =\langle \psi|T_{ab}|\psi \rangle -\langle 0|T_{ab}|0 \rangle this is for the usual Mink field modes and vac state. Why does normal ordering reduce to this expression, could anybody point me the way to...
  44. R

    Expectation of a Function of a RV in terms of PDF

    Homework Statement Find the expected value of cos(A+B) where A is a constant and B is a random variable with a pdf f(b). Present the answer in terms of f(b). The Attempt at a Solution I don't know how far I can go with the answer -- I have tried for a bit now to remove an integral with no...
  45. T

    Finding expectation of peicewise mixed distribution density function

    If I am given the CDF of a piecewise mixed distribution density starting from a and ending at b, would the expected value just be a + integral(all the pieces) ?
  46. S

    Expectation Value for a Function with Cusp

    Homework Statement In my homework assignment I have a wavefunction defined as \Psi(x)=N\exp(-|x|/a) and I am asked to find the expectation value of momentum squared in configuration space. Homework Equations \int\Psi*(x)\hat{p^2}\Psi(x)dx The Attempt at a Solution N is 1/\sqrt{a}...
  47. S

    How Does Hermitian Property Lead to \langle A^2 \rangle in Quantum Mechanics?

    I know that <Aψ|Aψ> = <A2>. Can anyone tell please tell me how you get one line to the another?
  48. S

    Expectation of position in a 2D system

    How does on calculate the expectation of the position operator x in a 2D infinite potential well (in the xy plane)? Do we only work with the Psi to the Hamiltonian in that particular coordinate when finding <Psi|x|Psi>?
  49. M

    Expectation Value Question with Unknown Operator

    Homework Statement Consider an observable A associated to an operator A with eigenvalues an. Using the formula <A> = ∫ψ*Aψ compute the expectation value of A for the following wave function: \Psi=\frac{1}{\sqrt{3}}\phi_{1}+\frac{1}{\sqrt{6}}\phi_{2}+\frac{1}{\sqrt{2}}\phi_{3} where...
  50. D

    Do expectation values vary with time?

    I'm a bit confused about the nature of probability conservation and expectation values. According to probability conservation, \frac{∂P(r,t)}{∂t}=0. Does that mean that expectation values e.g. <x>, <p> and <E> depend only on the position of the particle and not on time? Thanks
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