Two Variables Are Uncorrelated in All of the Cases Below $\left| \sigma _ { X Y } \right| \leq \sqrt { \sigma _ { X } ^ { 2 } \sigma _ { Y } ^ { 2 } }$

question 59

Short Answer

Two variables are uncorrelated in all of the cases below, with the exception of a. being independent.
b. having a zero covariance.
c. $\left| \sigma _ { X Y } \right| \leq \sqrt { \sigma _ { X } ^ { 2 } \sigma _ { Y } ^ { 2 } }$ .
d. $E ( Y \mid X ) = 0$ .

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Definitions:

Logic Circuit

An electrical circuit that performs logic operations, interpreting input signals to produce specific output signals based on logical rules.

Logic 1

A binary state representing a high or true condition in digital electronics, typically corresponding to a higher voltage level.

Truth Table

"A table listing that shows the state of a given output as a function of all possible input combinations."

Truth Table

A table used in logic and mathematics that shows the output of a particular function for all possible combinations of its inputs.