Math/Stat 394‚ Winter 2011 F.W. Scholz Central Limit Theorems and Proofs The following gives a self-contained treatment of the central limit theorem (CLT). It is based on Lindeberg’s (1922) method. To state the CLT which we shall prove‚ we introduce the following notation. We assume that Xn1 ‚ . . . ‚ Xnn are independent random variables with means 0 and 2 2 respective variances σn1 ‚ . . . ‚ σnn with 2 2 2 σn1 + . . . + σnn = τn > 0 for all n. 2 Denote the sum Xn1 + . . . + Xnn by Sn and observe
Premium Probability theory
A friend is one of life’s greatest gifts. In good times and bad times‚ a friend remains reassuring and faithful to the end. A friend lends a hand without being asked‚ encourages growth‚ and supports change. Time and distance can not diminish friendship. It is forever. My particular friend fits all of these characteristics and many more. She is a true friend under any circumstance. For many years my friend has been there for me. Her actions prove to me how much she really cares for other
Premium Friendship Love Interpersonal relationship
In my opinion Job’s friends took the wrong approach as to trying to figure out what caused the problem‚ and how it could be fixed. Some aspects of their advice could have been taken as words of wisdom‚ but the other aspects were ludicrous and should not have been taken seriously in the eyes of any Christian. The approach that they took was one in they were trying to determine exactly what Job did wrong. Some even thought that he deserved harsher punishment than what he was receiving. Once in the
Premium Devil Hell Satan
Could See Ryan Again Friendship is very important for everyone‚ especially me. During my studying from elementary school to university‚ I have lots of friends. Among those‚ there are a few friends who are my best friends. Now I would like to describe one of my best friends whose name is Ryan Thomas. The first reason I consider him as my best friend is that he has a very warm personality. He is so friendly when he meets me everywhere. For example‚ he always smiles politely at me. A smile that makes
Premium Friendship Scientific method Virtue
It is said a friend in need is a friend indeed. An ideal friend possesses all the qualities of head and heart. It is easy to befriend many but difficult to choose good friends. God gives us relatives by virtue of being born in a family‚ but friends we can choose. Rahul is my best friend. He is from U P.‚ a young lad of 18 with a thin body. But he has scholarly looks. He has a personality and manners that never fail to make an impression on others. His presence in a company always makes it lively
Premium Friendship Virtue
THE DEVOTED FRIEND By Oscar Wilde As it is known‚ Oscar Wilde was an Irish poet and writer who became popular because of his different forms of writing style‚ remembered as one of the greatest playwrights in the early 1890s. His work is characterized by two concepts of aesthetic: the moralizing aestheticism and the art for art’s sake‚ the second one being more prominent. Therefore‚ the stories action
Premium Short story Fiction Friendship
an air of pity and patronage. ’You are so very much like everything else in this country‚ inefficient‚ dirty‚ indifferent‚’ he murmured. The mirror smiled back at Sir Mohan. ’You are a bit of all right‚ old chap‚’ it said. ’Distinguished‚ efficient - even handsome. That neatly-trimmed moustache - the suit from Saville Row with the carnation in the buttonhole - the aroma of eau de cologne‚ talcum powder and scented soap all about you ! Yes‚ old fellow‚ you are a bit of all right.’ Sir Mohan
Premium English people Train station
The Hitchhikers Guide to the Internet 1 The Hitchhikers Guide to the Internet Ed Krol krol@uxc.cso.uiuc.edu Get any book for free on: www.Abika.com Get any book for free on: www.Abika.com The Hitchhikers Guide to the Internet 2 This document was produced through funding of the National Science Foundation. Copyright (C) 1987‚ by the Board of Trustees of The University of Illinois. Permission to duplicate this document‚ in whole or part‚ is granted provided reference is made
Free Domain Name System IP address Computer network
The poem "Let America Be America Again" by Langston Hughes purposefully is reminiscent of Walt Whitman’s "I Hear America Singing" in which Whitman is optimistic about this land of democratic opportunity. Hughes‚ however‚ writing from a black man’s perspective‚ is much less optimistic about what American has been or will be. While Whitman’s’ poem was very unstructured in blank verse‚ Hughes’s poem is more tightly controlled with rhyme‚ tone‚ rhetorical questions‚ and more unified with repeated anaphora
Premium Walt Whitman Question Rhetorical question
Friends - one word with a very beautiful meaning behind it. To most of us‚ friends are known as our pals‚ buddies or acquaintances. The more the merrier they always say. The more friends you have‚ the wider you horizon. With the ample presence of social networking sites these days such as Facebook and Twitter‚ it is much easier to be connected to people from the other end of the world than it used to be. With just a few clicks of the mouse‚ you will become friends or be connected virtually to other
Premium Social network service Reality Facebook