We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from Part I - Elements of Probability Theory
Published online by Cambridge University Press: 22 July 2022
An empirical average will converge, in some sense, to the corresponding expectation. This famous result, called the Law of Large Numbers, can be anticipated based on the concentration inequalities introduced in the previous chapter, but some appropriate notions of convergence for random variables need to be defined in order to make a rigorous statement. Beyond mere convergence, the fluctuations of an empirical average around the associated expectation can be characterized by the Central Limit Theorem, and are known to be Gaussian in some asymptotic sense. The chapter also discusses the limit of extremes such as the maximum of a sample.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
