The Conditional Expectation of Y Given X, E(Y $X = x )$

question 59

Multiple Choice

The conditional expectation of Y given X, E(Y $X = x )$ , is calculated as follows:

• A) \(\sum _ { i= 1 } ^ { k } Y _ { i } \operatorname { Pr } \left( X = x _ {i} \mid Y = y \right)\)
• B)E \([ E ( Y \mid X ) ] ]\)
• C) \(\sum _ { i= 1 } ^ { k } y _ { l } \operatorname { Pr } \left( Y = y _ {i} \mid X = x \right)\)
• D) \(\sum _ { i = 1 } ^ { k } E \left( Y \mid X = x _ { i } \right) \operatorname { Pr } \left( X = x _ { i } \right)\)

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Definitions:

Cash

Money in the form of coins or banknotes, especially that issued by a government.

Accruals

Accounting adjustments for revenues that have been earned but not yet recorded, and expenses that have been incurred but not yet recorded.

Explicit Interest

The interest rate stated in a contract or agreement, not including any compounding interest or hidden fees.

Capital

Financial assets or the value of financial assets used for the creation of goods or services or for investing.