Expectation Definition and 689 Threads

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. K

    Can Independence Simplify Calculating Expectation Values in Probability?

    Homework Statement f(x,y)=6a^{-5}xy^{2} 0≤x≤a and 0≤y≤a, 0 elsewhere Show that \overline{xy}=\overline{x}.\overline{y} Homework Equations \overline{x}=\int^{∞}_{-∞}{x.f(x)dx} The Attempt at a Solution \overline{x}=\int^{∞}_{-∞}{x.f(x)dx} =\int^{a}_{0}{x.6a^{-5}xy^{2}dx}...
  2. A

    Using operators and finding expectation value

    Homework Statement The expectation value of the time derivative of an arbitrary quantum operator \hat{O} is given by the expression: d\langle\hat{O}\rangle/dt\equiv\langled\hat{O}/dt\rangle=\langle∂\hat{O}/∂t\rangle+i/hbar\langle[\hat{H},\hat{O}]\rangle Obtain an expression for...
  3. A

    Does correlation affect the expectation value of a sum?

    We have for two random variables X and Y (one sum runs over j and one over k): E(X+Y) = ƩƩ(xj+yk)P(X=xk,Y=yk) = ƩƩxjP(X=xk,Y=yk) + ƩƩykP(X=xk,Y=yk) Now this can be simplified to obtain E(X+Y)=E(X)+E(Y) if we use that: P(X=xk,Y=yk) = P(X=xk)P(Y=yk), because then (and same goes the other...
  4. O

    MHB Conditional expectation proof question

    Here is a proof question: For two random variables X and Y, we can define E(X|Y) to be the function of Y that satisfies E(Xg(X)) = E(E(X|Y)g(Y)) for any function g. Using this definition show that E(X1 + X2|Y) = E(X1|Y) + E(X2|Y) So what I did was I plugged into X = X1 + X2 E(E(X1 +...
  5. C

    Expectation of a Joint Distribution

    The below gives all the information I was given. I'm pretty sure my answer is right, but a part of me isn't, and that's why I'm asking here. Homework Statement Let (X,Y) have the joint pdf: f_{XY}(x,y)=e^{-y}, 0 < x < y < \infty Find E(XY). Homework Equations...
  6. O

    MHB Double Expectation: Proving E(aX|Y) = aE(X|Y)

    For two random variables X and Y , we can define E(X|Y) to be the function of Y that satisfi es E(Xg(Y)) = E(E(X|Y)g(Y)) for any function g. Using this de finition show that E(aX|Y ) = aE(X|Y ). so according to the definition do i start with this?: E(aX|Y) = E(aE(X|Y)|Y) if so how do i...
  7. L

    Expectation: Is this proposition true or false?

    If X is a continuous random variable and E(X) exists, does the limit as x→∞ of x[1 - F(x)] = 0? I encountered this, but so far I have neither been able to prove this, nor find a counterexample. I have tried the mathematical definition of the limit, l'Hopital's rule, integration by parts, a...
  8. R

    Why we find expectation value?

    why we find expectation value? why do we take expectation value of sime entity? and how come we know that our expected value is correct
  9. J

    Product rule of derivative of expectation values

    Hello, first post here. I am preparing for my Introductory Quantum Mechanics course, and in the exam questions, we are asked to use Ehrenfest's theorem to show that \frac{d}{dt}\langle \vec{r}\cdot \vec{p} \rangle = \langle 2T-\vec{r}\cdot \nabla V \rangle Now, from other results...
  10. fluidistic

    Expectation value of kinetic energy (QM)

    Homework Statement In a QM problem I must calculate the expectation value of the kinetic energy, namely ##\langle \Psi _c ,\frac{ \hat { \vec p } ^2}{2m} \Psi _c \rangle##. Where ##\Psi _c=ce^{-\alpha x^2}##. Homework Equations ##\int _{-\infty}^\infty \exp \{ -a x^2 +bx \} dx =...
  11. B

    Spin expectation values in x and y direction

    I have found what I think is the correct answer I just want to check an assumption. The magnetic field points in the +ve z-direction. We are given the initial state vector \left| A \right\rangle_{initial}=\frac{1}{5}\left[ \begin{array}{c}3\\4\end{array} \right] Am I right in thinking that...
  12. L

    Vacuum expectation values of combinations of ##a^\dagger## and ##a##

    I am slightly confused on how do we calculate vacuum expectation values of product of creation and annihilation operators for bosons, e.g. ##\langle 0| a_{k_1} a^\dagger_{k_2} a_{k_3} a^\dagger_{k_4} |0 \rangle## If i commute ##k_3## and ##k_4##: $$\langle 0| a_{k_1} a^\dagger_{k_2}...
  13. P

    Rolling motion- experimental data differs from expectation

    Homework Statement An experiment was done to test the validity of the equation a = 2/3 g sin∅ for a rolling cylinder. A hockey puck was rolled down a wooden ramp at 5 different inclination angles, and the time it took to roll down the length of the board was recorded. ∅ was found using...
  14. Roodles01

    Expectation value in the ground state

    Homework Statement . Hi, could someone look at the attachment & comment on whether I'm anywhere near getting the expectation value correct, please. In the grnd state; 1. terms such as AA†A†A, with lowering operator on RHS has zero expectation value, 2. terms such as AA†A†A† with uneven...
  15. tomwilliam2

    Expectation values of Kin energy in Bra-Ket notation

    Homework Statement Confirm explicitly that ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x \Psi \rangle## cannot be negative. Homework Equations ##-i\hbar \frac{\partial}{\partial x} = \hat{p}_x## The Attempt at a Solution i seem to get: ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x...
  16. Roodles01

    Expectation value at ground state

    I realize that at ground state of a harmonic oscillator the energy will be at zero. I'm assuming that the expectation value will also be at zero. Could someone confirm this & possibly explain just a little more. Thank you
  17. B

    Show the expectation value is non negative

    Homework Statement The kinetic energy is given by \left\langle E_{kin} \right\rangle = \frac{\left\langle \widehat{p}^2 \right\rangle}{2m} In Dirac notation we have \left\langle E_{kin} \right\rangle = \frac{1}{2m} \left\langle \widehat{p}\Psi | \widehat{p}\Psi \right\rangle Homework...
  18. P

    Probability & Expectation Value of X + Y

    we have variables X,Y with f(m,n)=P(X=m,Y=n) with f(0.1)=0.1 f(1.0)=0.1 f(1.1)=0.344 find the expectation value E(X+Y) i need help because i don't how to start to solve this , if i begin with the definition of the expected value i can't do anything any ideas?
  19. P

    Statistics expectation problem involving circle.

    Hi, Homework Statement A circle of radius r is as shown in the attached diagram. I am asked to first express X as a function of θ, then to compute E(X). It is also stated that θ obeys U[0,2π]. Homework Equations The Attempt at a Solution Through simple trigonometry I have found X...
  20. P

    Statistics expectation of discrete variable.

    Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...
  21. M

    Is <A> Always Zero for Anti-Hermitian Operators in Real Functions?

    I'm stuck on a question in atkins molecular quantum mechanics 4e (self test 1.9). If (Af)* = -Af, show that <A> = 0 for any real function f. I think you are expected to use the completeness relation sum,s { |s><s| = 1. I'm sure the answer is simple but I'm stumped.
  22. A

    Calculating Marginal Density and Expectation of Project Cost

    Homework Statement Let the joint density of the material and labor cost of a project be modeled by fx,y(u,v) = 2v*e-v*(2+u) u,v ≥ 0 = 0 otherwise a) find marginal density of X and Y b) find E(Y)...
  23. Barioth

    Correlation and mathematical expectation question

    Hi, I have these 2 problem, that I'm not so sure how to handle. 1-Let X_1,X_2,...,X_n independant Random variable that all follow a continuous uniform distribution in (0,1) a) Find E[Max(X_1,X_2,...,X_n)] b) Find E[Min(X_1,X_2,...,X_n)] where E is for the mathematical...
  24. M

    A simple conditional expectation question

    Let v be a random variable distributed according to F(.). Let X be a set containing the objects x1 and x2. Suppose E(v|x1) = b AND E(v|x2) = b (The expected value of v conditional on x1 is b, etc) where b is some constant. Does it follow that E(v|x1,x2) = b? If so, why...
  25. G

    Expectation value of potential energy of Ideal gas

    Homework Statement Say you have a large column of gas with insulating walls standing on the Earth's surface, which is L high and at room temperature (25degC) at the interface of the surface and column. Assuming the potential energy on the gas is only duel to gravity, U = mgx where x is the...
  26. C

    Vacuum expectation value and lorenz (trans) invariance

    Hi! I've seen it stated that because of Lorenz and translational invariance \langle 0| \phi(x) |0 \rangle has to be a constant and I wondered how to formally verify this?
  27. T

    Expectation values for Hydrogen

    Ok, so I'm a little confused about why <p> = 0 for Hydrogen in the ground state. If someone explain the reasoning behind this, I'd greatly appreciate it. Also, and more importantly, does that mean that <p> = 0 for Hydrogen in other states as well? If not, how would you go about finding <p>...
  28. H

    Solving Difficult Expectation with Normal Distribution

    Hi everyone, I have been struggling with an expectation for a while. It is seems very difficult (if not impossible) to find an analytical expression, but all hints and suggestions would be most appreciated. Here goes. I want to find an analytical expression (i.e. solve the integral) for the...
  29. A

    Evaluating the Expectation for $\mu$ and $\hat{\mu}$

    Homework Statement X_{1} , ..., X_{5} \textit{ iid } N( \mu , 1) \textit{ and } \hat{\mu} = \bar{X} where L( \mu , \hat{\mu} ) = | \mu - \hat{\mu} | The Attempt at a Solution E[ | \mu - \hat{\mu} | ] = 0 since E(\hat{\mu}) = \mu Am I missing something? Seems too easy...
  30. P

    Quantum time corr: expectation value of particle motion in Schro. pic

    Homework Statement The expectation value of motion of a particle over a time interval t-to is C(t,to) = <0|x(t)x(to)|0> (product of position operators in Heisenberg representation for ground state harmonic oscillator) Homework Equations Schrodinger picture: <ψ(t)|Ω|ψ(t)> =...
  31. V

    Expectation value of non-physical observable

    Homework Statement This may be incredibly obvious, but I just need to check. Of course we all know that physical observables must yield real expectation values. What if you tried to calculate, say, <xV(d/dx)>, where x is the position, d/dx is a first derivative, and V is the potential? This...
  32. B

    Expectation of Covariance Estimate

    So I'm trying to take the expectation of the covariance estimate. I'm stuck at this point. I know I have to separate the instances where i=j for the terms of the form E[XiYj], but I'm not quite sure how to in this instance. The answer at the end should be biased, and I'm trying to...
  33. N

    Expectation value of a dynamical variable problem.

    Homework Statement Why does the extra phase factor cancel out? Is it because you are multiplying the wave-function with the extra phase factor by its conjugate and if so, why should it matter that the extra phase factor is independent of x? All relevant information, the solution and equation...
  34. A

    Expectation value in unpertubed basis

    I have a question regarding an exercise I am doing. It is an electron confined to move on a cylinder and I am asked to: "Find the expectation value of Ly and Lz" in the unperturbed basis. I am just not sure what is meant by the expectation value in a basis? I know what the expectation value is...
  35. N

    Integration by parts of derivative of expectation value problem

    Homework Statement I don't know how the writer of the book took integral of the first statement and got the second statement? Can anybody clarify on this? Homework Equations Given in the photoThe Attempt at a Solution When I took the integral I just ended up with the exact same statement but...
  36. B

    Fourier Transfrom and expectation value of momemtum operator

    Homework Statement Using <\hat{p}n> = ∫dxψ*(x)(\hat{p})nψ(x) and \hat{p} = -ihbar∂x and the definition of the Fourier transform show that <\hat{p}> = ∫dk|\tilde{ψ}(k)|2hbar*k 2. The attempt at a solution Let n = 1 and substitute the expression for the momentum operator. Transform the...
  37. S

    Time Dependent expectation value in momentum space

    Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values hω/2 or 3hω/2, each with a probability of one-half. The average values of the momentum <p> at time t = 0 is √mωh/2. This information...
  38. A

    Why am I getting different results when using the law of total expectation?

    Suppose a box initially contains 1 red marble and 1 black marble and that, at each time n = 1, 2, ..., we randomly select a marble from the box and replace it with one additional marble of the same color. Let X_n denote the number of red marbles in the box at time n (note that X_0 = 1). What is...
  39. L

    Conditional expectation in statistics

    Hi, I am trying to show that if the E[W|X]=0 then the Cov (W,X)=0. Using the def of variance, and given that E[W] is zero, I get that Cov is equal to: E[WX]-E[W * E(X)] using conditional expectation: E [E(WX|X)] -E[x]E[W]= E[X E[W|X]]-E[X]E[E(W|X)]=0 I am not sure if...
  40. S

    Expectation of Position of a Harmonic Oscillator

    Hey, My question is on determing the expectation value of position of the Harmonic Oscillator using raising and lowering operators, the question is part d) below: I have determined the position operator to be: \hat{x}=\sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger}) and so the...
  41. A

    Expectation values for angular momentum

    Consider a quantum system with angular momentum 1, in a state represented by the vector \Psi=\frac{1}{\sqrt{26}}[1, 4, -3] Find the expectation values <L_{z}> and <L_{x}> I'm reviewing my quantum mechanics; I had a pretty horrible course on it during undergrad. I feel like this should be...
  42. S

    Is the Expectation Value of the y-Component of Spin Represented by Sy?

    Hey, I'm having trouble interpreting a question, as the solutions say something different... Anyways the question part d) below: So we want to determine the expectation value of the y-component of the electron spin on the eigenstate of Sx, now I would of thought this was given by...
  43. S

    Simple expectation value calculation

    Homework Statement This problem comes from the second edition of Griffiths's, Introduction to Quantum Mechanics. Given the Gaussian Distribution: p(x) = Aec(x-a)2 find <x>, that is, the expectation (or mean) value of x. Clearly, to do this you evaluate the following integral: ∫xp(x)dx on...
  44. L

    [QM] Expectation value in spin-1/2 state

    Homework Statement Basically I need to produce a state for a spin-1/2 particle such that the expectation value of <Jz> = 0 where <Jz> is for a spin-1 particle. Homework Equations Jz = (1 0 0, 0 0 0, 0 0 -1) <--[3x3] matrix The Attempt at a Solution I don't quite understand how to do this...
  45. A

    Expectation values of spin operators in changing magnetic field

    Homework Statement Homework Equations The Attempt at a Solution I have totally no idea how to solve this question. But I find it somehow similar to the Larmor precession problem. Therefore I try to solve my problem by referring to that. Are there any mistakes if I do it like...
  46. A

    Expectation value of momentum times position particles in a box

    Homework Statement What is the expectation value of <p*x> aka the momentum times the position operator, for a particle in a box. Homework Equations Psi(x) = root(2/l) sin (n∏x/l) P= -ih(bar)d/dx X=x The Attempt at a Solution All integrals are from 0 to L I'm typing this on a playbook so I...
  47. F

    Infinite square well expectation value problem

    Homework Statement A particle in an infinite box is in the first excited state (n=2). Obtain the expectation value 1/2<xp+px> 2. The attempt at a solution Honestly, I don't even know where to begin. I assumed V<0, V>L is V=∞ and 0<V<L is V=0 I tried setting up the expectation...
  48. C

    Question about expectation values.

    Is it possible to define operators to find the expectation value of position for a Gaussian wave packet. Similar to finding raising and lowering operators for the harmonic oscillator in terms of position and momentum and then using those to find <x> and <p>. But I was just wondering if this...
  49. P

    Expectation operator - linearity

    Homework Statement Show that the expectation operator E() is a linear operator, or, implying: E(a\bar{x}+b\bar{y})=aE(\bar{x})+bE(\bar{y}) Homework Equations E(\bar{x})=\int_{-\infty}^{+\infty}xf_{\bar{x}}(x)dx With f_{\bar{x}} the probability density function of random variable x...
  50. C

    Question about expectation value.

    It seems that the energy expectation value is independent of time. I did it for an infinite square well. And when you time evolve your wave function the time evolution cancels when you complex conjugate it and then do the integral. <E>=<ψ|E|ψ> it seem like this might always...
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