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Machine Learning Intermediate 2 min read

What is independently and identically distributed?

A statistical concept describing random variables that are independent and have the same probability distribution

Independently and identically distributed, or i.i.d., refers to a set of random variables that have two key properties: they are independent, meaning the value of one variable does not affect the others, and they are identically distributed, meaning they all follow the same probability distribution

Imagine flipping multiple coins that are identical and do not influence each other - each coin flip is an independent event with the same probability of landing heads or tails, making the outcomes independently and identically distributed

In a study on the average height of a population, if the heights of individuals are independently and identically distributed, it means that the height of one person does not affect the height of another, and they all follow the same distribution, allowing for more accurate statistical analysis

This concept is used in statistical modeling, machine learning, and data analysis to make assumptions about the behavior of random variables and to simplify complex problems

A common misconception is that independently and identically distributed variables must be normally distributed, when in fact they can follow any probability distribution

The concept of independently and identically distributed variables has its roots in probability theory and statistics, dating back to the early 20th century

i.i.d. independent and identically distributed random variables identically distributed independent variables

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