April 2008
Intermediate
832 pages
26h 2m
English
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CHAPTER A Random Variables
The presentation in the book relies on some basic concepts from probability theory and random variables. For the benefit of the reader, we shall motivate these concepts whenever needed as well as highlight their relevance in the estimation context. In this way, readers will be introduced to the necessary concepts in a gradual and motivated manner, and they will come to appreciate their significance away from unnecessary abstractions. In this initial chapter, we collect several concepts of general interest. These concepts complement well the material in future chapters and will be called upon at different stages of the discussion.
A.1 VARIANCE OF A RANDOM VARIABLE
We initiate our presentation with an intuitive explanation for what the variance of a random variable means. The explanation will help the reader appreciate the value of the least-mean-squares criterion, which is used extensively in later chapters.
Consider a scalar real-valued random variable x with mean value 
and variance 
, i.e.,
where the symbol E denotes the expectation operator. Observe that we are using boldface letters to denote random variables, which will be our convention in ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.