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:

Inventory Analysis

The examination and evaluation of stock or inventory to ensure optimal stock levels, turnover rates, and minimized waste.

Linear Programming

A mathematical method for determining a way to achieve the best outcome, such as maximum profit or lowest cost, in a given mathematical model for some list of requirements represented as linear relationships.

Open System

An entity or process that interacts with its environment by exchanging information, material, or energy.

Outputs

The ultimate outputs, whether products, services or outcomes, produced by a system, process, or organization.