# conditional expectation

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## conditional expectation

[kən′dish·ən·əl ‚ek‚spek′tā·shən]
(mathematics)
If X is a random variable on a probability space (Ω, F,P), the conditional expectation of X with respect to a given sub σ-field F′ of F is an F′-measurable random variable whose expected value over any set in F′ is equal to the expected value of X over this set.
(statistics)
The expected value of a conditional distribution.
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The author has organized the main body of his text in seven chapters devoted to random variables and stochastic processes, conditional probability and conditional expectation, normal processes and covariance stationary processes, counting processes and Poisson processes, renewal counting processes, and a wide variety of other related subjects.
For readers not familiar with the conditional expectation theorem, this result could also be written in the following form, which seems intuitively reasonable:
It is the product of the conditional expectation and its conditioning joint probability:
Although I may not subscribe to Jarocinski and Smets's interpretation of the conditional expectation of output or inflation as an indicator of monetary conditions, I do agree with their conclusion that housing is at the core of the business cycle, so it should have a prominent role in the formulation of monetary policy.
Given a realisation of a spatio-temporal point process X of spikes and given a trajectory of the path Y, the solution of the nonlinear filtering problem is the conditional expectation E[[LAMBDA]|X,Y] which is not explicitly available.
21] as the derivative of the conditional expectation in (9), evaluated at the mean of [x.
If the loss is proportional to the square of the forecast error then we have a quadratic loss function and the forecast which minimises the expected loss is the conditional expectation or mean of the forecast density.
The conclusion, drawn from the existing literature, is that while there is no generally accepted model of the stochastic discount factor, its conditional expectation must be relatively stable in order to explain the stability of the riskless real interest rate.
To employ this approach, take the conditional expectation of (9) to get:
Tables I and II show the values of the conditional expectation function, h(z).
The analytical tools for measuring the economic value associated with the exercise of the intellectual property right in a foreign nation are the conditional expectation of marginal revenues and the conditional expectation of marginal costs.
More specifically they show how some ideas often considered complex, such as conditional expectation, can be developed in a systematic way by considering their definition as orthogonal projections in convenient Hilbert spaces.

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