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Old 01-20-2019, 04:18 PM
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htlin htlin is offline
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 610
Default Re: What is the definition of expectation with respect to data set

Originally Posted by Fromdusktilldawn View Post
Thank you for the answer.

However, there is still a distinction between a vector, and a set of vectors.

In other words, {1} is not the same as 1.

However, in multiple locations in the textbook, the dataset is represented as a set. For example, at the bottom of page 8.

My question is, is the dataset a vector consisting of pairs, or a set of pairs?

In other words, the distinction between [(1,2), (3,4)]^T versus {(1,2), (3,4)}. I don't really understand the notation D = (x_1, y_1), (x_2, y_2)...(x_N,y_N) because as it is written it is neither a vector nor a set.

I apologize in advance if I am being too rigorous and nitpicky
The data set is a set of pairs in this book. While the set is by definition not ordered, the data set is more often "ordered by index"---and thus conveniently represented by a (pair of) matrix (like what we did in Chapter 3).

Hope this helps.
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