Download e-book for iPad: All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman

By Larry Wasserman

ISBN-10: 0387402721

ISBN-13: 9780387402727

WINNER OF THE 2005 DEGROOT PRIZE!

This publication is for those that are looking to study likelihood and records speedy. It brings jointly a number of the major rules in sleek records in a single position. The e-book is appropriate for college kids and researchers in records, machine technology, facts mining and laptop learning.

This publication covers a wider variety of themes than a customary introductory textual content on mathematical data. It comprises sleek subject matters like nonparametric curve estimation, bootstrapping and type, themes which are often relegated to follow-up classes. The reader is thought to grasp calculus and a bit linear algebra. No past wisdom of chance and data is needed. The textual content can be utilized on the complex undergraduate and graduate point.

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Additional resources for All of Statistics: A Concise Course in Statistical Inference (Springer Texts in Statistics)

Example text

J jx(x)= 21 211 ydy=-x(1-x) 21 2 4 f(x,y)dy=-x 4 X2 8 for -1 ::; x ::; 1 and fx(x) = 0 otherwise. 29 Definition. 7) and we write X II Y. Otherwise we say that X and Yare dependent and we write X IQ6OO' Y. 7) for all subsets A and B. Fortunately, we have the following result which we state for continuous random variables though it is true for discrete random variables too. 30 Theorem. Let X and Y have joint PDF fx,Y. Then X IT Y if and only if fx,Y(x, y) = fx(x)Jy(y) for all values x and y. 31 Example.

The notation x dF (x) deserves some comment. We use it merely as a J convenient unifying notation so we don't have to write Lx xf(x) for discrete 48 3. Expectation random variables and I xf(x)dx for continuous random variables, but you should be aware that I x dF (x) has a precise meaning that is discussed in real analysis courses. To ensure that lE(X) is well defined, we say that lE(X) exists if IxldFx (x) < 00. Otherwise we say that the expectation does not exist. 2 Example. Let X '" Bernoulli(p).

2. _ Appendix Recall that a probability measure IF' is defined on a a-field A of a sample space n. A random variable X is a measurable map X : n -+ R Measurable means that, for every X, {w: X(w) <::: x} E A. 14 Exercises 1. Show that 44 2. Random Variables 1 ,----------, 1 (y - 1, 1) (O ,y) (1, Y - 1) °o This is the case 0 :::; y °o 1 < 1. 1 This is the case 1 :::; Y :::; 2. 6. 48. Ay consists of all points square below the line X2 = Y - Xl. (Xl,X2) in the 2. Let X be such that J1D(X = 2) = J1D(X = 3) = 1/10 and J1D(X = 5) = 8/10.

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All of Statistics: A Concise Course in Statistical Inference (Springer Texts in Statistics) by Larry Wasserman


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