chapter 4 companion and outline
This page contains companion resources and an outline for chapter 4 of the book An Introduction to Real-Time Computing for Mechanical Engineers, and it therefore lacks most of chapter 4’s contents. While some sections of the book are fully available on this site, many are not. Please consider purchasing a copy from the MIT Press.
Statistics
Whereas probability theory is primarily focused on the relations among mathematical objects, statistics is concerned with making sense of the outcomes of observation (Skiena 2001). However, we frequently use statistical methods to estimate probabilistic models. For instance, we will learn how to estimate the standard deviation of a random process we have some reason to expect has a Gaussian probability distribution.
Statistics has applications in nearly every applied science and engineering discipline. Any time measurements are made, statistical analysis is how one makes sense of the results. For instance, determining a reasonable level of confidence in a measured parameter requires statistics.
A particularly hot topic nowadays is machine learning, which seems to be a field with applications that continue to expand. This field is fundamentally built on statistics.
A good introduction to statistics appears at the end of Ash (2008). A more involved introduction is given by Jaynes et al. (2003). The treatment by Kreyszig (2011) is rather incomplete, as will be our own.
Populations, samples, and machine learning
Estimation of sample mean and variance
Confidence
Student confidence
Regression
Problems
Online resources for Chapter 4
No online resources.