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
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing ApplicationsBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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.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.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.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.
PROBLEMS
Sufficient Statistics and UMVU Estimation
9.1 For N iid Poisson samples, use the definition of sufficiency to find a sufficient statistic for parameter α.
9.2 For N iid uniform samples with pdf 
, use the factorization theorem to find a sufficient statistic for 
.
9.3 Repeat Problem 9.2 for N iid gamma samples to find a sufficient statistic for 
.
9.4 Derive the expectations in (9.30) for the minimum and maximum.
9.5 Find the minimal sufficient statistic from M iid samples of the chi-square distribution with parameter N.
9.6 Use the ratio approach in (9.34) to find the minimal sufficient statistic from N iid samples of the Poisson random variable with parameter α.
9.7 For the exponential random variable with location parameter c:
(9.398) 
show that the minimal sufficient statistic for c (with fixed λ) is X(1) from N iid samples.
9.8 For N iid Laplace samples with parameters 
, find a minimal sufficient statistic for (a) α (with fixed) and then (b) μ (with α = 1).
9.9 For N iid uniform ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
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.