- #1

lode

- 1

- 0

In what cases can I move from

E[ Y(X) ]

to

E[ Y(E(X))]

someone has any idea?

is there a text You recomend on the topic?

thanks..

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- Thread starter lode
- Start date

- #1

lode

- 1

- 0

In what cases can I move from

E[ Y(X) ]

to

E[ Y(E(X))]

someone has any idea?

is there a text You recomend on the topic?

thanks..

- #2

SW VandeCarr

- 2,175

- 80

In what cases can I move from

E[ Y(X) ]

to

E[ Y(E(X))]

someone has any idea?

is there a text You recomend on the topic?

thanks..

I think you mean E(Y|X).

Can you combine X and R where R ( for 'residual') includes all other extraneous conditions on Y? If so, then write P(X)+P(R)-P(X)P(R)=P(X') assuming X and R are independent.

Then use Bayes' Theorem:

P(Y|X')=P(X'|Y)P(Y)/P(X')

The validity if this approach assumes that P(Y|X') includes all conditions on Y.

EDIT: You could of course simply find P(Y|X) the same way, but this does not give you as good a description of the behavior of Y when you know of other conditions on Y. E(Y|X') is the value of Y|X' when P(Y|X') is maximal.

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