Two Random Variables Are Independently Distributed If Their Joint Distribution

question 33

Essay

Two random variables are independently distributed if their joint distribution is the product of their marginal distributions. It is intuitively easier to understand that two random variables are independently distributed if all conditional distributions of Y given X are equal. Derive one of the two conditions from the other.

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Definitions:

Gain/Loss

The financial result from the sale of assets or investments, measured as the difference between the selling price and the purchase price.

Purchased

Acquired by paying money or its equivalent; involves obtaining ownership of a good or service in exchange for monetary value.

MAGI

MAGI stands for Modified Adjusted Gross Income, a measure used in the U.S. tax code to determine eligibility for certain tax benefits by modifying the adjusted gross income with specific additions or deductions.

Net Investment Income

The income received from investment assets (like stocks, bonds, mutual funds) after deducting related expenses.