New PDF release: All of Statistics: A Concise Course in Statistical Inference

By Larry Wasserman

ISBN-10: 0387217363

ISBN-13: 9780387217369

ISBN-10: 1441923225

ISBN-13: 9781441923226

This ebook is for those who are looking to research chance and statistics quick. It brings jointly some of the major principles in smooth information in a single position. The e-book is appropriate for college kids and researchers in information, machine technology, facts mining and computing device learning.

This ebook covers a wider variety of subject matters than a regular introductory textual content on mathematical facts. It contains sleek issues like nonparametric curve estimation, bootstrapping and class, themes which are frequently relegated to follow-up classes. The reader is believed to understand calculus and a bit linear algebra. No past wisdom of likelihood and information is needed. The textual content can be utilized on the complicated undergraduate and graduate level.

Larry Wasserman is Professor of statistics at Carnegie Mellon collage. he's additionally a member of the guts for automatic studying and Discovery within the university of computing device technological know-how. His learn components contain nonparametric inference, asymptotic idea, causality, and purposes to astrophysics, bioinformatics, and genetics. he's the 1999 winner of the Committee of Presidents of Statistical Societies Presidents' Award and the 2002 winner of the Centre de recherches mathematiques de Montreal–Statistical Society of Canada Prize in data. he's affiliate Editor of The magazine of the yank Statistical Association and The Annals of Statistics. he's a fellow of the yankee Statistical organization and of the Institute of Mathematical Statistics.

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Additional info for All of Statistics: A Concise Course in Statistical Inference

Example text

We define the probability function or probability mass function for X by fx(x) = IP'(X = x). Thus, f x (x) :;0. 0 for all x E lR and Li f x (Xi) = l. Sometimes we write f instead of Ix. The CDF of X is related to fx by Fx(x) = IP'(X ::; x) = L fX(Xi). 10 Example. 6 is 1/4 fx(x) = { 1/2 1/4 o x = 0 x = 1 x = 2 otherwise. 2. _ 3 A set is countable if it is finite or it can be put in a one-to-one correspondence with the integers. The even numbers, the odd numbers, and the rationals are countable; the set of real numbers between 0 and 1 is not countable.

Then x = IA(x) where IA(x) = 1 if L J IE(IA(X)) = IA(x)fx(x)dx = 49 fx(x)dx = JF'(X E A). In other words, probability is a special case of expectation. 7 Example. Let X Unif(O, 1). Let Y = r(X) = eX. Then, rv IE(Y) = 10{I eX f(x)dx = 11 0 eXdx = e - 1. Alternatively, you could find jy(y) which turns out to be jy(y) = l/y for 1 < y < e. Then, IE(Y) = J~e y f(y)dy = e - 1. 8 Example. Take a stick of unit length and break it at random. Let Y be the length of the longer piece. What is the mean of Y?

1 Introduction Statistics and data mining are concerned with data. How do we link sample spaces and events to data? The link is provided by the concept of a random variable. 1 Definition. A random variable is a mapping! that assigns a real number X(w) to each outcome w. At a certain point in most probability courses, the sample space is rarely mentioned anymore and we work directly with random variables. But you should keep in mind that the sample space is really there, lurking in the background.

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All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman

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