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. J

    I need the dirac notation expectation value explaining to me please?

    Hi, I find a lot of the time in QM i have been calculating things blindly. Take the expectation value for instance. I have worked this out in integral form plenty of times, but haven't really understood why I'm doing what I'm doing. I looked up wikipedia and apparently, for a measurable...
  2. M

    Difference between expectation value and probabilty

    Homework Statement Psi(x) = Ax -a<x<a I am trying to find the probability that my measured momentum is between h/a and 2h/a Homework Equations I have normalized A= sqrt(3/(2a^3)) I know that if I was finding the expected momentum I would use \int\Psi * p \Psi dx The...
  3. O

    Fundamental question about conditional Expectation

    Homework Statement I am familiar with the following kind of conditional expectation expression: \mathbb{E}[Y|X=x], where X and Y are random variables. I am wondering what the following conditional expectation stands for: \mathbb{E}[Y|X] How these two are related? How the second...
  4. pellman

    Why is the Green's function equal to the vacuum expectation of the field?

    In QFT expressions such as these hold: real scalar: \Delta_F(x-x')\propto\langle 0| T\phi(x)\phi(x')|0\rangle 4-spinor S_F(x-x')]\propto\langle 0| T\psi(x)\bar{\psi}(x')|0\rangle where T is the time-ordering operation and the proportionality depends on the choice of normalization...
  5. M

    Why isn't my LaTeX code displaying properly on PhysicsForums.com?

    I'm not sure why PhysicsForums.com isn't displaying my latex properly so I have attached a PDF of the question. Homework Statement Show that, for a 3D wavepacket, \frac{d\langle x^2 \rangle}{dt} $=$ \frac{1}{m}(\langle xp_{x} \rangle+\langle p_{x}x \rangle) The Attempt at a...
  6. H

    Method of Indicators for computing expectation

    Hi, I have the following problem: Suppose you have a coin that has chance p of landing heads. Suppose you flip the coin n times and let X denote the number of 'head runs' in n flips. A 'head run' is defined as any sequence of heads. For example the sequence HHTHHHHHTTTTHHTHT contains 4 head...
  7. O

    Derivative of an Expectation value/Ehrenfest theorem

    Show that (d/dt)<x^2>=(1/m)(<x(p_x)>+<(p_x)x>) For a three dimensional wave packet Homework Equations 1. <O>=Int_v(d^3r)(psi*Opsi), where O is some operator Ehrenfest Theorem: 2. ihbar(d/dt)<O>=<[O,H]>+<(partial)(d/dt)O>, H is a hamiltonian. The Attempt at a Solution I...
  8. O

    How Does the Time Evolution of Expectation Shape Scientific Understanding?

  9. C

    Iterative expectation of continuous and discrete distributions

    Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...
  10. C

    Can someone help me with expectation values for the radial wavefunction?

    Show that the expectation value of Lz is -2h for the radial wavefunction Y2,-2. ? Can someone do this?
  11. B

    Expectation value of Coulomb potential depends on relative spin

    Homework Statement Show that the expectation value of the Coulomb potential v(\vec{r_1},\vec{r_2})=\frac{e^2}{|\vec{r_1}-\vec{r_2}|}, between two electrons depends on the relative orientation of spin of the two electrons. Assume each electron is in the product state form...
  12. H

    Expectation value of momentum in discrete states

    Is there any way of proving <p> = 0 for a discrete (bound) state given it's wave function? I've seen proofs using the hermitian properties of p but I'm interested in proving that the integral of Psi*(x) Psi'(x) is identically zero regardless of Psi(x) as long as it's a solution of Schroedinger's...
  13. J

    Simple quantum problem - find eigenvalues, probabilities, expectation value?

    hi, not strictly homework as my course doesn't get going again for a couple of weeks yet, but suppose I have a system with quantum number l=1 in the angular momentum state u = \frac{1}{\sqrt{2}} \left(\begin{array}{cc}1\\1\\0\end{array}\right) and I measure Lz, the angular momentum component...
  14. D

    Joint expectation of two functions of a random variable

    Ok I am not sure if I should put this question in the homework category of here but it’s a problem from schaums outline and I know the solution to it but I don’t understand the solution 100% so maybe someone can explain this to me. Let X and Y be defined by: \begin{array}{l} X = \cos \theta...
  15. I

    Is the expectation value of this commutator zero?

    If I have H=p^2/2m+V(x), |a'> are energy eigenkets with eigenvalue E_{a'}, isn't the expectation value of [H,x] wrt |a'> not always 0? Don't I have that <a'|[H,x]|a'> = <a'|(Hx-xH)|a'> = <a'|Hx|a'> - <a'|xH|a'> = 0 ? But if I calculate the commutator, I get: <a'|[H,x]|a'> = <a'|-i p \hbar /...
  16. E

    Conditional expectation of three exponential distributed r.v.

    I've been struggling with this problem for more than 4 days now: Let A, B and C be exponential distributed random variables with parameters lambda_A, lambda_B and lambda_C, respectively. Calculate E [ B | A < B < C ] in terms of the lambda's. I always seem get an integral which is...
  17. D

    Understanding Expectation Values in Quantum Mechanics

    Let A be an observable (opeator), and we're assuming that for a given state psi(x), the value of A is given by A acting on psi(x), namely - A|psi>. Also we assume that - P(x) = |psi(x)|^2 So, I'de expect the Expectation value of A to be defined like so: <A> = Integral[-Inf:+Inf]{ P(x) A...
  18. D

    Calculate expectation value of H'

    Homework Statement Calculate the expectation value of \hat{H}' in the state \psi(x,t=0). \hat{H}'=k(\hat{x}\hat{p}+\hat{p}\hat{x}) \psi(x,t=0)=A(\sqrt{3}i\varphi_{1}(x)+\varphi_{3}(x)), where A=\frac{1}{2} Homework Equations The Attempt at a Solution I know it's found by...
  19. K

    Computing vacuum expectation values

    I have small question computing vacuum expectation values here http://www.cns.gatech.edu/FieldTheory/extras/SrednickiQFT03.pdf" from Mark Srednicki. My problem is with equation 210 on the pdf page 69. In the second line of 210, where does the second term come from? Z(J) and W(J) are defined...
  20. K

    Expectation of an absolute value

    Homework Statement I have E(a) = 0, E(b) = x but E(|a+b|)=?? where E is the expectations operator and x is a known constant which is greater than zero. Homework Equations Any one know how I would go about determining E(|a+b|)?
  21. O

    Relationship between two random variables having same expectation

    Homework Statement Say, it is known that E_X[f(X)] = E_X[g(X)] = a where f(X) and g(X) are two functions of the same random variable X. What is the relationship between f(X) and g(X)? Homework Equations The Attempt at a Solution My answer is f(X) = g(X) + h(X) where E_X[h(X)] =...
  22. T

    Integration help for expectation of a function of a random variable

    Homework Statement Hello, have a stats question I am hoping you guys can help with. The expectation of a function g of a random variable X is: E[g(X)] = \int^{\infty}_{-\infty} g(x)fx(x)dx where fx is the pdf of X. For example, the particular expectation I am considering right now...
  23. K

    What is average deviation from expectation?

    In the book "The mathematic of Gambling", the author considers a fair coin with 50% getting head and 50% for tail. The expectation of such coin, of course, will be zero. Here is what I read from the text, it reads Consider the fair game example mentioned earlier in the chapter (fair coin)...
  24. I

    Expectation value for angular momentum

    Homework Statement A wavefunction of angular momentum states is given: \psi = \frac{1}{\sqrt{7}}|1,-1\rangle + \frac{\sqrt{35}}{7}|1,0\rangle+\sqrt{\frac{1}{7}}|1,1\rangle Calculate \langle \psi| L_{\pm} |\psi \rangle and \langle 1,1|L_+^2|\psi\rangle3. Attempt at a solution. If the...
  25. R

    Quantum Mechanics Expectation

    Quantum Mechanics "Expectation" Homework Statement 1. Calculate the expectation value <p_{x}> of the momentum of a particle trapped in a one-dimensional box. 2. Find the expectation value <x> of the position of a particle trapped in a box L wide.Homework Equations \psi...
  26. W

    Proving Expectation: X and Y Random Variables

    hello! can any1 please help me with the following proofs? thanks let X and Y be random variables. prove the following: (a) if X = 1, then E(X) = 1 (b) If X ≥ 0, then E(X) ≥ 0 (c) If Y ≤ X, then E(Y) ≤ E(X) (d) |E(X)|≤ E(|X|) (e) E(X)= \sumP(X≥n)
  27. M

    Derivation of the velocity of an expectation value

    Homework Statement I am trying to derive for myself the velocity of the expectation value from the information given, specifically that <x> = \int_{-\infty}^{\infty}x|\Psi (x,t)|^2 dt (1) Eq (1) can be transformed into, \frac{d<x>}{dt} =...
  28. D

    QM Measurements - probability, expectation value

    Homework Statement What are the possible results and their probabilities for a system with l=1 in the angular momentum state u = \frac{1}{\sqrt{2}}(1 1 0)? What is the expectation value? ((1 1 0) is a vertical matrix but I can't see how to format that) Homework Equations The...
  29. D

    Conditional expectation on multiple variables

    How to compute E[X|Y1,Y2]? Assume all random variables are discrete. I tried E[X|Y1,Y2] = \sum_x{x p(x|y1,y2) but I'm not sure how to compute p(x|y1,y2] = \frac{p(x \cap y1 \cap y2)}{p(y1 \cap y2)} If it is correct, how can I simplify the expression if Y1 and Y2 are iid?
  30. C

    Expectation Value For a Given Wave Function

    Homework Statement Find the expectation value of x (Find <x>) given the wave function: \psi(x)=[sqrt(m*alpha)/h_bar]e^[(-m*alpha*|x|)/(h_bar)^2] This wave function represents the single bound state for the delta-function potential. It's the solution to the shrodinger equation given the...
  31. S

    Expectation of terms in double summation

    Does anybody help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve. [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex] where f(k,j) and [\tex]\theta_{k,j}[\tex] are some...
  32. S

    Calculating Expectation Value of Angular Momentum Squared for Hydrogen Atom

    Homework Statement Consider a hydrogen atom whose wave function at time t=0 is the following superposition of normalised energy eigenfunctions: Ψ(r,t=0)=1/3 [2ϕ100(r) -2ϕ321(r) -ϕ430(r) ] What is the expectation value of the angular momentum squared? Homework Equations I know...
  33. H

    Expectation value of spin operators.

    Homework Statement If an electron is in an eigen state with eigen vector : [1] [0] what are the expectation values of the operators S_{x}, and S_{z} Interpret answer in terms of the Stern-Gerlach experiment. The Attempt at a Solution Im not too sure how to calculate the...
  34. T

    Two problems about expectation

    1. If X is uniform distributed in (0,pi), what is E(X|sinX)? 2. Suppose X and Y are Gaussian random variables N(0,sigma_x) and N(0,sigma_y). what is the distribution of E(X-Y|2X-Y) Can anyone help? thanks
  35. R

    Normalised wavefunction to calculate the expectation

    Do we have to use normalised wavefunction to calculate the expectation and probability of finding the particle? If yes, why?
  36. M

    Quantum mechanical expectation value

    I'm trying to calculate the expectation value of the momentum squared (p^2) of the harmonic oscillator ground state. The integral involves the second derivative of a Gaussian (exponential of a negative squared term) Then the integral involves, after working it out, an x^2 term times...
  37. LarryS

    Probability Density or Expectation Value?

    In a paper in Physical Review A, the author discusses a wave function for one particle, Ψ(r,t), where r is the position vector. He writes "The probability distribution for one-particle detection at a point r is given by |<r|Ψ >|2 ". Is that correct? The above expression looks, to me...
  38. C

    Why is the Linearity of Expectation Used in This Equation?

    Hi I'm going through some presentation material and i can't understand how the following has been derived \sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})] Could someone point me in the right direction on why this makes sense ? Thanks
  39. D

    Expectation and Variance for Continous Uniform RV

    Homework Statement 8. Suppose that X and Y are independent continuous random variables, and each is uniformly distributed on the interval [0,1] (thus the pdfs for X and Y are zero outside of this interval and equal to one on [0,1]). (a) Find the mean and variance for X+Y. (b) Calculate...
  40. K

    Expectation values for a harmonic oscillator

    Homework Statement I need to find <x>, <x2>, <p>, and <p2> for a particle in the first state of a harmonic oscillator. Homework Equations The harmonic oscillator in the first state is described by \psi(x)=A\alpha1/2*x*e-\alpha*x2/2. I'm using the definition <Q>=(\int\psi1*Q*\psi)dx...
  41. M

    Energy expectation values of harmonic oscillator

    I'm looking at a question... The last part is this: find the expectation values of energy at t=0 The function that describes the particle of mass m is A.SUM[(1/sqrt2)^n].\varphi_n where I've found A to be 1/sqrt2. The energy eigenstates are \varphi_n with eigenvalue E_n=(n + 1/2)hw...
  42. L

    Calculating Expectation Value of Kinetic Energy in 3D Bound State

    ok. this is an easy enough thing to prove in one dimension but my question seems to be 3 dimensional and it's causing me some hassle: show the expectation value of the kinetic energy in a bound state described by the spherically symmetric wavefunction \psi_T(r) may be written \langle...
  43. L

    Help With Expectation of Y(X) & X Following Gaussian Law

    I have two random variables Y and X and Y is dependent of X, though X is not the only source of variability of Y. With fixed X=x, Y(x) follows gaussian law. X also follows gaussian law. In what cases can I move from E[ Y(X) ] to E[ Y(E(X))] someone has any idea? is there a text...
  44. W

    Expectation value of position of wavepacket

    Hello, this is just a general question, how is <x^2> evaluated, if <x> = triple integral of psi*(r,t).x.psi(r,t).dr (this is the expectation value of position of wavepacket) Is it possible to square a triple integral? Is <x^2> the same as <x>^2 ? I'm only wondering how the squared works...
  45. S

    Exploring Constant Observable Expectations: Measuring in a Lab Setting

    If the expectation of some observable is constant then can it be measured at Lab.
  46. N

    Expectation Values and Operators

    I've never seen an expectation value taken and would greatly appreciate seeing a step by step of how it is done. Feel free to use any wavefunction, this is the one I've been trying to do: In the case of \Psi=c1\Psi1 + c2\Psi2 + ... + cn\Psin And the operator A(hat) => A(hat)\Psi1 =...
  47. M

    Conditional expectation of exponential distribution.

    I have been stuck at this calculation. There are two exponential distributions X and Y with mean 6 and 3 respectively. We need to find E[y-x|y>x] I keep getting it negative, which is clearly wrong. Anybody wants to try it?
  48. T

    Expanding expectation equation; Linear algebra

    Kalman Filter - Covariance Matrix Kalman Filter Problem Homework Statement I have the following expectation formula: P_k=E\{\left[(x_k-\hat{x}^-_k)-K_k(H_k x_k+v_k-H_k \hat{x}^-_k)\right]\left[(x_k-\hat{x}^-_k)-K_k(H_k x_k+v_k-H_k \hat{x}^-_k)\right]\}2. The attempt at a solution I'm told...
  49. Q

    Time-dependence of expectation value <x> in a quantum harmonic oscillator?

    Find the time dependence of the expectation value <x> in a quantum harmonic oscillator, where the potential is given by V=\frac{1}{2}kx^2 I'm assuming some wavefunction of the form \Psi(x,t)=\psi(x) e^{-iEt/\hbar} When I apply the position operator, I get: <x>=\int_{-\infty}^\infty...
  50. A

    Can I do expectation like this

    Many thanks in advance Suppose x is normal variable x~N(a,b) and y=160*x^2 I need calculate E(y)=∫yf(y)d(y) f(y) is the density function of y how can I write it as an integral of x since we know x's distribution, I mean use the density function of x to substitute the original integral...
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