This set of lecture notes on general relativity has been expanded into a textbook,Spacetime and Geometry: An Introduction to General Relativity, available for purchase online or at finer bookstores everywhere. About 50% of the book is completely new; I've also polished and improved many of the...
microeconomic_theory - Lecture Notes ,2018-02微观经济学理论-课堂讲稿.pdf,1 August, 2002/Revised: February 2018 1This lecture notes are for the purpose of my teaching and convenience of my students in class. Contents I Preliminary Knowledge and Methods
Theorem 14 (The Central Limit Theorem (CLT)) Let X1 , . . . , Xn be iid with mean ? and variance σ 2 . Let X n = n?1 n i=1 Xi . Then Zn ≡ Xn ? ? Var(X n ) where Z ? N (0, 1). In other words, z n→∞ √ n(X n ? ?) = σ Z lim P(Zn ≤ z ) ...
means weak convergence (or convergence in distribution), and N(m, v) denotes the normal distribution with mean m ∈ R and variance v >0. This is a most rudimentary example of an “invariance principle.” Here we have a limit theoremwhere the limiting distribution depends on the ...
Lecture19:Conditional Probability&Expectation STAT205Lecturer:Jim Pitman Scribe:Saurabh Amin<amins@berkeley.edu> This set of notes is a revision of the work of Charles C.Fowlkes.Reference:[1], section4.1.19.1Definition of Conditional Expectation We present the definition of conditional ...
This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Book...