November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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4.11 TRANSFORMATIONS OF RANDOM VECTORS
The previous techniques for transforming one random variable to another random variable can be extended to multiple random variables. We will not derive all the results in detail, but instead present the main ideas behind transformations of continuous random variables, and then summarize the results for various types of transformations, including those for discrete random variables.
Consider random vector 
and its transformation to random vector 
according to 
where 
are known functions (possibly nonlinear). These functions could be strictly increasing, strictly decreasing, nonmonotonic, may contain flat regions, or may have some combination of these features over various intervals. The functions might also map to a subset of the elements of 
to 
. We first consider the case where the N functions are either strictly increasing or strictly decreasing. For ...
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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.