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. N

    Quantum expectation value (griffiths)

    Homework Statement If x is the position of a particle then the expectation value of x, <x> is : (I got lazy and just copied an image from Wiki, just pretend <x> is on the lhs of the eqn) When Griffith derives an expression for d<x> / dt, he uses the fact that dx/dt is zero, since "the wave...
  2. M

    Expectation Values for momentum and a particle in a square well

    Homework Statement Calculate the expectation values of p and p2 for a particle in state n=2 in a square well potential. Homework Equations \Psi(x,y) = (2/L)*sin(n1\pix/L)*sin(n2\piy/L) p= -i\hbar\partial/\partialx The Attempt at a Solution \int\Psip\Psidxdy...
  3. K

    Quantum Mechanics - Finding expectation value

    Homework Statement Find the expectation value of position as a function of time. Homework Equations This is in the latter half of a multi-part question, previously we were given that: Eqn 1: Ψ(x, t) = A(ψ1(x)e−iE1t/h¯ + iψ2(x)e−iE2t/h¯) and in an even earlier part: Eqn 2: ψn(x) =...
  4. C

    Conditional Expectation of Sum

    Hi everyone, I have a feeling the following property is true but I can't find it stated in any textbook/online reference. Maybe it's not true... Can someone verify/disprove this equation? E(A+B|C) = E(A|C) + E(B|C)
  5. H

    Angular Momentum and Expectation Values

    Can anyone explain to me why the only time that the expectation of L^2 operator and the expectation value of L_3^2 are equal only when there is no angular dependence? And what does this mean? Does this have something to do with being restricted to the z-axis which is what L_3 is associated...
  6. M

    Expectation of a random variable

    Homework Statement I'm wondering how I go about calculating the expectation of a random variable? Is it a different process for a discrete and a continuous? Can you show me an example? Say Poisson and expoential? Also, in the formula Var(X) = E[X^2] - (E[X])^2 how does one...
  7. R

    Electron Energies in Atoms: Fixed Values or Expectation Values?

    Hi. First post. I'm trying to understand if electronic energy levels have fixed values, or merely fixed expectation values (in the latter case, orbital electrons could have any energy and it's only the average that would be fixed). Here's my argument for the latter. If it's incorrect, could...
  8. F

    Proof: Operators with same expectation value

    Given some state \left|\psi\right\rangle, and two operators \hat{A} and \hat{B}, how do you prove that if \langle\psi|\hat{A}|\psi\rangle = \langle\psi|\hat{B}| \psi\rangle then \hat{A} = \hat{B} ?
  9. P

    Is the expectation value of momentum of a stationary state zero?

    Given a stationary state H \psi = E \psi \Rightarrow \left(-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x)\right)\psi = E\psi Firstly is it true that \left<p\right> = \frac{\hbar}{i}\int\psi^* \frac{\partial \psi}{\partial x} dx= 0 ?? If it is, how do we prove it?
  10. O

    Does E(e^{-X}) = 0 imply X = \infty almost surely for X \geq 0?

    Does the following make sense: E(e^{-X}) = 0 \Rightarrow X = \infty\quad a.s. ? (Intuitively yes, but mathematically?) Thank you in advance for your help! :-) /O
  11. S

    What is the expectation value of Sz for the ground state?

    Homework Statement Kindly take a look at the attachment for the problem statement. Homework Equations Schrodinger Equation: H psi = E psi The Attempt at a Solution For Part A: H psi = E psi S= 1/2 So energy of ground state is -1/2.K.H.hcross Could you tell me if I am on the...
  12. N

    Conditional expectation of exponential random variable

    For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value from searching in internet I found that E{X|X>a}=a+E{x} but I can not prove it Help please
  13. N

    Conditional expectation of exponential random variable

    Homework Statement For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value Homework Equations The Attempt at a Solution
  14. R

    Squaring uniform/normal distribution and expectation

    Suppose X is a uniformly distributed random variable on an interval [-a,a] for some real a. Let Y=X^2. Then what could you say about this distribution of Y? I have no idea how to think about this distribution. Also how could we compute the expectation of Y? I know that E[X]=0 but what could I...
  15. J

    Expectation of X*Y= E(XY)

    Hi everyone, I was searching an answer for E(XY), where X and Y are two dependent random variables, number of observations n=21 and Sum(x*y)= 1060.84. Can somebody help me? It's not mentioned, but I think that each x and y of the distributions have the same probability to occur. Thank you.
  16. L

    Can posts be deleted on online forums?

    Homework Statement how do you delete a post?
  17. T

    Position expectation value in harmonic oscillator

    Hello, I want to find <xftf|x(t)|xiti> in harmonic oscillator. I tried to insert the complete set of energy eigenstates to the right and the left side of x(t), but it yields somewhat more complicated stuff. Thank you
  18. K

    Hydrogen atom expectation of r^2 check

    I haven't posted any of my working for this as I only want to check my answer. Q. For a hydrogen atom with n=2, l=1, m=0 calculate <r^2> My answer = 0.75 * a^2 where a is the bhor radius. Am I right?
  19. C

    Expectation value of total energy

    Homework Statement given a wavefuntion \Psi = (1/sqrt50) (3\mu1 + 5\mu2 - 4\mu3) what is the expectation value of the total energy? My thoughts were to calculate <\Psi|\hat{}H|\Psi> but the previous part to the question asks for the probability of each outcome(which I know how to...
  20. N

    Why the minima of potential of classical Lagrangian called ''vacuum expectation''?

    Please teach me this: Why the minima of potential of classical Lagrangian is called the ''vacuum expectation value of Phi(field function)''.Is it really a vacuum expectation value of field operator at the vacuum states(at this state,the potential part of classical Lagrangian equals zero)...
  21. P

    Expectation value of spin in an Ising lattice

    Homework Statement I have to show that (the question says deduce from the fact that magnetization is monotonically increasing and a concave function for h>0) \left< \sigma^2_{j} \right> - \left \sigma_j \right>^2 \geq 0 and \left< \left( \sigma^_{j} \right> - \sigma_j \right)^2 \right> \geq 0...
  22. L

    Probability question involving generating functions and expectation

    Homework Statement Hi, I'm stuck on the very last part of 5.b https://www.maths.ox.ac.uk/system/files/attachments/PaperC2003.pdf Homework Equations The Attempt at a Solution I can't prove the inequality, would it be right to say the expected premium would be...
  23. I

    Expectation values of spin operators

    Hi, I've found the expectation value of Sz, which is hbar/2 (|\psiup|2 - |\psidown|2) by using the formula: <Si> = <\psi|Si\psi> where i can bex, y or z and \psi is the 'spinor' vector. I tried to find Sx using the same formula, however, I could only get as far as: hbar/2 ((\psiup)*\psidown...
  24. T

    Expectation Values/Bra-ket Problem

    Concerning expectation values... Also, the derivation in terms of bra-ket rather than wage function would be appreciated. Where \psi is the system state Knowing that <A>\psi=<\psi|A|\psi> And A is comprised of a complete eigenvector set \phij w/ corresponding eigenvalues aj How do you...
  25. P

    Physicsal meaning of Expectation of two variables

    I have a problem understanding why I need the expectation of two variable which are dependent. What is the physical meaning of this E[xy]. I know that E[X] is the likelihood f finidng say a particle from a experiment repreated N time atthe same place. What Kind of physical meaning exist of two...
  26. N

    Expectation Value of O†: Is It Equal to Complex Conjugate of <O>?

    Homework Statement Hi Say I have an operator O, and I find its expectation value <O>. Now, if I wish to find the expectation value of O† († denoting Hermitian conjugate), then will this just equal the complex conjugate of <O>? Niles.
  27. Z

    Harmonic Oscillator Expectation Values

    Homework Statement A particle of mass m that is confined to a harmonic oscillator potential V(x) = \frac{1}{2} m \omega^2 x^2 is described by a wave packet having the probability density, |\Psi (x,t) |^2 = \left(\frac{m\omega}{\pi\hbar} \right )^{1/2}\textrm{exp}\left[-\frac{mw}{\hbar}(x -...
  28. H

    Calculating E[x] for f(x)=e^-2|x| distribution in the reals (x e R)

    I want to calculate E[x] of the following continuous distribution having density: f(x)=e^-2|x| for x in the reals (x e R) I did the calculation with integral bounds infinity and minus infinity, are these the right bounds to use since we are only told x e R? I got 0 as the answer, can someone...
  29. R

    Probability Theory - Expectation Problem

    Homework Statement Discrete random variables X and Y , whose values are positive integers, have the joint probability mass function , (, ) = 2−−. Determine the marginal probability mass functions () and (). Are X and Y independent? Determine [], [ ], and [ ]. The Attempt at a Solution...
  30. J

    Complex conjugate of the expectation value of momentum

    Homework Statement Compute the complex conjugate of <p> using eq 1.35 (<p>=∫ψ*(h/i)∂/∂x ψ dx) and prove that <p> is real (<p>=<p>*) Homework Equations equation 1.35 is given above The Attempt at a Solution to take the c.c. don't i just add a minus to the i and switch the stars like...
  31. S

    Conditional Expectation Question (Probability Theory)

    Homework Statement (Question is #6 on p.171 in An Introduction to Probability and Statistics by Ruhatgi & Saleh) Let X have PMF Pλ{X=x} = λxe-λ/x!, x=0,1,2... and suppose that λ is a realization of a RV Λ with PDF f(λ)=e-λ, λ>0. Find E(e-Λ|X=1) The Attempt at a Solution The...
  32. S

    Sample variance expectation

    It is defined that the population variance is S^{2}= \frac{1}{N-1}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2} or \sigma^{2}= \frac{1}{N}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2}. Also that the V\left[\bar{y}_{n}\right] = \frac{N-n}{N}\frac{S^{2}}{n} = \left(\frac{1}{n} -...
  33. C

    Expectation value of the angular momentum operator

    Homework Statement Hey forum, I copied the problem from a pdf file and uploaded the image: http://img232.imageshack.us/img232/6345/problem4.png What is the probability that the measurement of L^{2} will yield 2\hbar^{2} Homework Equations \left\langle L^{2} \right\rangle = \left\langle \Psi...
  34. M

    Tough Conditional Expectation Problem

    Homework Statement Suppose that $Y$ is a random variable, $\mathcal{G}$ a $\sigma$-algebra, $E|Y| < \infty$. Show that $Y = E(Y|\mathcal{G})$ a.s. (a.s. = almost surely). Homework Equations We're given $Y$ integrable. The Attempt at a Solution It's recommended as a hint to prove...
  35. G

    Expectation Values of x & p for Wavefunction u(x,0)

    Homework Statement A particle is represented(at t=0) by the wavefunction u(x,0) = A(a^2 - x^2) if -a<x<a = 0 otherwise Determine <x> & <p>. It is given in the book that in this case <p> \neq m*d/dt<x>. Could someone please tell me the reason...
  36. P

    Expectation value of a vector?

    Homework Statement Prove that for a particle in a potential V(r) the rate of change of the expectation value of the orbital angular momentum L is equal to the expectation value of the torque: d/dt <L> = <N> Where N = r x(-del V) N, r, and L are vectors. Homework Equations...
  37. E

    Analytic determination of Expectation, variance

    Hi, I want to proof what the distribution will be when I apply a normal distributed x to a linear function y = a*x + b. What will be the mean and the variance of y ? The expectations can be calculated than with this formula ( probably with this formula what i want can be proofed with...
  38. X

    Expectation value of X and Y component of angular momentum

    Homework Statement Show: <Jx>=<Jy>=0 Homework Equations Jx=1/2(J++J-) Jy=1/2(J+-J-) The Attempt at a Solution <jm l Jx l jm> = < jm l 1/2 J+ l jm> + < jm l j- l jm > = < jm l h/2 sqrt [(j-m)(j+m+1)] + h/2sqrt[(j+m)(j+m+1) l jm > i am not sure how to apply the next step
  39. N

    QM: Calculating Expectation Values

    Homework Statement Hi Say I have the following number: \left\langle {\psi _i |A|\psi _j } \right\rangle 1) First of all, am I correct when saying that \left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle ^* where...
  40. J

    Expectation value of the sum of two random variables

    Homework Statement The expectation value of the sum of two random variables is given as: \langle x + y \rangle = \langle x \rangle + \langel y \rangle My textbook provides the following derivation of this relationship. Suppose that we have two random variables, x and y. Let p_{ij}...
  41. T

    Markov Chain Conditional Expectation

    Hello, in relation to Markov chains, could you please clarify the following equations: In particular, could you please expand on why the first line is equal. Surely from , along with the first equation, this implies that: I just don't see why they are all equal. Please could you...
  42. T

    Stats - Conditional Expectation

    Homework Statement [PLAIN]http://img222.imageshack.us/img222/2781/statsqk.jpg Homework Equations f_{X} (x) = \int^{\infty}_{-\infty} f_{X,Y} (x,y)\;dy f_{Y} (y) = \int^{\infty}_{-\infty} f_{X,Y} (x,y)\;dx f_{X|Y} (x|y) = \frac{f_{X,Y} (x,y)}{f_Y (y)} f_{Y|X} (y|x) =...
  43. K

    Hamiltonians and Expectation Values and Ehrenfest's theorum, OH MY ()

    Homework Statement (a) Let Q be an operator which is not a function of time, abd Let H be the Hamiltonian operator. Show that: i(hbar)(\delta<q> / dt =<[Q,H]> Here <q> is the expectation value of Q for any arbirtary time-dependent wave function Psi, which is not necessarily an...
  44. G

    Expectation of a function of X and Y

    Homework Statement Find E[X^Y], where X and Y are independent random variables which are uniform on [0,1]. Homework Equations The Attempt at a Solution I know that to get E[f(x)] for a function of one continuous random variable X, you integrate xf(x) between minus and plus infinity...
  45. D

    Expectation Value: My Understanding vs. Prof.

    My understanding was that the expectation value of an observable H for a state |a> is just <a|H|a>. But in a homework problem, my prof. used <H> = <a|H|a>/<a|a>. I'm a little confused by the discrepancy, why the discrepancy?
  46. D

    Is the Product of Expectation Values Always True in Quantum Mechanics?

    In quantum mechanics, when is this true \langle\psi|AB|\psi\rangle=\langle\psi | A|\psi\rangle\langle\psi |B|\psi\rangle ? In probability theory, when the two variables are independent, the mean value of the product is the product of the mean values. What about QM?
  47. T

    Calculating expectation value of angular kinetic energy

    Homework Statement the origial question given is: Show that the difference in energies between 2s and 2p radial wavefunctions is equal to the energy of the angular part of the 2p wavefunction, and thus that they have the same overall energy. hints given:a)use virial theorem to determine...
  48. facenian

    Expectation value no sense result

    Homework Statement Evaluate <x^2> for the wave function \psi(x)=\int_{-\infty}^{\infty}dk exp(-|k|/k_0)exp(ikx) My calculation yields a negative answer and I can't find my error Homework Equations...
  49. T

    Quantum System: Expectation Value

    Homework Statement |O> = k |R1> + 1/9 |R2> a) Find k if |O> has already been normalized, and b) then the expectation value. The Attempt at a Solution a) To Normalise: |(|O>)|2 = (1/9 |R2> + k |R1>).(1/9 |R2> - k|R1>) = 1/81|R2>2 - k2|R1>2 = 1 I just assumed that |k| = (1-(1/81))0.5, but...
  50. T

    Calculating Expectation Value for z component of angular momentum

    Homework Statement Calculate the expectation value for the z component of angular momentum (operator is (h/i)(d/dx)) for the function sinx*e^(ix). Homework Equations I think the only one relevant is the expectation value: <a> = integral[psi*(a)psi] / integral[psi*psi] where psi* is...
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