Two Random Variables X and Y Are Independently Distributed If $\operatorname { Pr } ( Y = y \mid X = x ) = \operatorname { Pr } ( Y = y )$

question 3

Short Answer

Two random variables X and Y are independently distributed if all of the following conditions hold, with the exception of a. $\operatorname { Pr } ( Y = y \mid X = x ) = \operatorname { Pr } ( Y = y )$ .
b. knowing the value of one of the variables provides no information about the other.
c. if the conditional distribution of $Y$ given $X$ equals the marginal distribution of $Y$ .
d. $\quad E ( Y ) = E [ E ( Y \mid X ) ]$ .

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Definitions:

Bulimia Nervosa

An eating disorder involving episodes of binge eating followed by purging to prevent weight gain.

Anorexia Nervosa

The diagnosis involves having an alarmingly low weight, an extreme apprehension about weight gain, and a distorted perception of one’s body shape or size.

Bulimia Nervosa

An eating disorder characterized by episodes of binge eating followed by compensatory behaviors such as self-induced vomiting, fasting, excessive exercise, or misuse of laxatives.

Binge-purge Patterns

A cycle of excessive eating episodes followed by behaviors to prevent weight gain, such as vomiting, commonly associated with bulimia nervosa.