# 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. ### Understanding Conditional Expectation, Variance, and Precision Matrices

My question relates to subsection 2.2.1 of [this article][1]. This subsection recalls the work of Lindgren, Rue, and Lindström (2011) on Gaussian Markov Random Fields (GMRFs). The subsection starts with a two-dimensional regular lattice where the 4 first-order neighbours of $u_{i,j}$ are...
2. ### Expectation of a sum of random variables

\begin{align*} E[(A+B)^2]&=E[A^2+2AB+B^2]\\ &=E[A^2]+2E[AB]+E[B^2]\\ &=2E[AB]+E[B^2]. \end{align*} Can the terms ##2E[AB]## and ##E[B^2]## be simplified any more? Thanks, friends.
3. ### I Computing the expectation of the minimum difference between the 0th i.i.d.r.v. and ith i.i.d.r.v.s where 1 ≤ i ≤ n

Problem :Let ##X_0,X_1,\dots,X_n## be independent random variables, each distributed uniformly on [0,1].Find ## E\left[ \min_{1\leq i\leq n}\vert X_0 -X_i\vert \right] ##. Would any member of Physics Forum take efforts to explain with all details the following author's solution to this...
4. ### POTW Is the Finite Expectation of Powers Satisfied by Nonnegative Random Variables?

Suppose ##X## is a nonnegative random variable and ##p\in (0,\infty)##. Show that ##\mathbb{E}[X^p] < \infty## if and only if ##\sum_{n = 1}^\infty n^{p-1}P(X \ge n) < \infty##.

25. ### Solve the probability distribution and expectation problem

This is the problem; Find my working to solution below; find mark scheme solution below; I seek any other approach ( shorter way of doing it) will be appreciated...
26. ### A QFT with vanishing vacuum expectation value and perturbation theory

In This wikipedia article is said: "If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a...
27. ### A Probability via Expectation and Callen's criterion

In the thermal interpretation, the collection of all q-expectations (and q-correlations) is the state of a system. The interpretation of q-expectations is used only to provide an ontology, the apparent randomness is analysed and explained separately. This may be non-intuitive. Callen's criterion...
28. ### I How to calculate expectation and variance of kernel density estimator?

This is a question from a mathematical statistics textbook, used at the first and most basic mathematical statistics course for undergraduate students. This exercise follows the chapter on nonparametric inference. An attempt at a solution is given. Any help is appreciated. Exercise: Suppose...
29. ### Expectation of amount of money won in a game

This is what I did: Let Y = number of sixes occurred when ##n## dice are thrown Y ~ B (n, 1/6) E(Y) = ##\frac{1}{6}n##Let Z = amount of money received → Z = ##\frac{1}{2}Y## E(Z) = E(1/2 Y) = 1/2 E(Y) = ##\frac{1}{12}n##I got the answer but I am not sure about my working because I didn't...

Hi all, I found this notation of expectation values in a NMR text. In class, I learned that expectation values are given by $$<\hat{X}>=\int_{-\infty}^\infty\psi^*x\psi dx$$ why does this textbook divide by the integral of probability density ##\int \psi^*\psi dx##?
31. ### Expectation value of momentum operator

I know that the eigenstates of momentum operator are given by exp(ikx) To construct a real-valued and normalized wavefunction out of these eigenstates, I have, psi(x) = [exp(ikx) + exp(-ikx)]/ sqrt(2) But my trouble is, how do I find the expectation value of momentum operator <p> using this...

39. ### I How to prove the Cauchy distribution has no moments?

How can I prove the Cauchy distribution has no moments? ##E(X^n)=\int_{-\infty}^\infty\frac{x^n}{\pi(1+x^2)}\ dx.## I can prove myself, letting ##n=1## or ##n=2## that it does not have any moment. However, how would I prove for ALL ##n##, that the Cauchy distribution has no moments?
40. ### Quantum Mechanics Hydrogen Atom Expectation Value Problem

I can not solve this problem: However, I have a similar problem with proper solution: Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...
41. ### MHB Counterfactual Expectation Calculation

$\newcommand{\doop}{\operatorname{do}}$ Problem: (This is from Study question 4.3.1 from Causal Inference in Statistics: A Primer, by Pearl, Glymour, and Jewell.) Consider the causal model in the following figure and assume that $U_1$ and $U_2$ are two independent Gaussian variables, each with...
42. ### I Relation with Hessian and Log-likelihood

I would like to demonstrate the equation (1) below in the general form of the Log-likelihood : ##E\Big[\frac{\partial \mathcal{L}}{\partial \theta} \frac{\partial \mathcal{L}^{\prime}}{\partial \theta}\Big]=E\Big[\frac{-\partial^{2} \mathcal{L}}{\partial \theta \partial...
43. ### Do i need to calculate the expectation value of the Hamiltonian?

Hi, I have a question which asks me to use the generalised Ehrenfest Theorem to find expressions for ##\frac {d<Sx>} {dt}## and ##\frac {d<Sy>} {dt}## - I have worked out <Sx> and <Sy> earlier in the question. Since the generalised Ehrenfest Theorem takes the form...
44. ### QHO: Time dependant expectation value of the potential energy

Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...
45. ### A Expectation of a Fraction of Gaussian Hypergeometric Functions

I am looking for the expectation of a fraction of Gauss hypergeometric functions. $$E_X\left[\frac{{}_2F_1\left(\begin{matrix}x+a+1\\x+a+1\end{matrix},a+1,c\right)}{{}_2F_1\left(\begin{matrix}x+a\\x+a\end{matrix},a,c\right)}\right]=?$$ Are there any identities that could be used to simplify or...
46. ### A Expectation Value of a Stabilizer

Given that operator ##S_M##, which consists entirely of ##Y## and ##Z## Pauli operators, is a stabilizer of some graph state ##G## i.e. the eigenvalue equation is given as ##S_MG = G## (eigenvalue ##1##). In the paper 'Graph States as a Resource for Quantum Metrology' (page 3) it states that...
47. ### Expectation value of an angular momentum with a complex exponent

I am struggling to figure out how to calculate the expectation value because I am finding it hard to do something with the exponential. I tried using Euler's formula and some commutator relations, but I am always left with some term like ##\exp(L_z)## that I am not sure how to get rid of.
48. ### Time Derivatives of Expectation Value of X^2 in a Harmonic Oscillator

I can show that ##\frac{d}{dt} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{1}{m} \langle \psi (t) \vert PX+XP \vert \psi (t) \rangle##. Taking another derivative with respect to time of this, I get ##\frac{d^2}{dt^2} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{i}{m...
49. ### Expectation value of angular momentum

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩
50. ### MHB Cdf, expectation, and variance of a random continuous variable

Given the probability density function f(x) = b[1-(4x/10-6/10)^2] for 1.5 < x <4. and f(x) = 0 elsewhere. 1. What is the value of b such that f(x) becomes a valid density function 2. What is the cumulative distribution function F(x) of f(x) 3. What is the Expectation of X, E[X] 4. What is...