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:

INF Treaty

The Intermediate-Range Nuclear Forces Treaty, a 1987 agreement between the United States and the Soviet Union to eliminate all nuclear and conventional missiles and their launchers with ranges of 500-5,500 km.

Intermediate-range Nuclear Missiles

Ballistic missiles with a range capability between 1,000 and 5,500 kilometers, designed to deliver nuclear warheads to intermediate distances.

Apartheid

A policy or system of segregation or discrimination on grounds of race, implemented in South Africa from 1948 until the early 1990s, which severely restricted the rights of the non-white population.

Constructive Engagement

A diplomatic policy of engaging with a nation in a positive manner to encourage changes in policies or behavior, often used in contexts of human rights or economic reform.