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
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Sir Mohan Lal looked at himself in the mirror of a first class waiting room at the railway station. The mirror was obviously made in India. The red oxide at its back had come off at several places and long lines of translucent glass cut across its surface. Sir Mohan smiled at the mirror with 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
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Reflections For the past few weeks‚ we had been having English classes with Madam Diana. She had been a great teacher. Alright‚ maybe great is not the right adjectives to describe her. Madam Diana is a fabulous teacher! English classes always bore me‚ but not with Madam Diana. Different approaches are used by her in teaching us‚ leaving a big impact on us. As a part of learning process‚ we are also assigned with weekly reflections which requires us to reflect on whatever we have learnt throughout
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He is lionized with proper cause; he is flawless‚ deserving of compliments in such quantity to become white noise. Physically‚ he is near impeccable‚ yet when first meeting him‚ nothing spectacular is noticed. The more he is looked upon‚ the more that is found to admire. Indeed‚ he has his flaws‚ but only the obvious ones‚ only the insignificant ones. When one becomes proficient at gazing longingly into his beautiful eyes‚ it is as if an answer to a silent prayer is found. His gaze is like a sword—carefully
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In the Nathaniel Hawthorne’s The Scarlet Letter‚ Hester Prynne is convicted of adultery and condemned to wear a scarlet “A” and suffer essential excommunication from society. Hester and her young daughter‚ Pearl‚ find themselves outcasts in the Puritan society of seventeenth-century Boston. On the surface‚ this novel’s tale is the opposite of proto-feminist‚ a term applied to works that show the emergence of modern feminist concepts. Via the actions and characteristics main characters‚ or perhaps
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poses as a direct threat to women’s safety and self-esteem in various ways. The most commonly overlooked form of sexism is the “Friend-zone”‚ a manifestation of misogynistic ideology created by vapid petulant men who refuse to take “no” for an answer‚ and is used as an excuse for aggressive male dominance as well as sexual and domestic violence. According to the friend
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I leave this letter today to you in hope that you will find it when you have become big enough to learn about your world. Today I have an important revelation to make‚ the world you grow up in might not be the same as what I had. You know me as your granddad but to the world‚ I am a scientist who gave the world the most destructive weapon ever to exist. What will change your world is science. Science is something objective‚ it comes with a goal. But its application is numerous and sometimes unethical
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The Scarlet Letter In the “Scarlet Letter” Nathaniel Hawthorne describes the consequences for sinning. The story takes place in a puritan community in Boston‚ Massachusetts in the 17th century. In the story the main character‚ Hester Prynne‚ commits adultery with the Reverend mr.Dimmsdale. As a result of their actions‚ Pearl is born. Hester is punished to wear the scarlet letter A‚ which stands for Adultery‚ on her breast. Hester’s husband‚ Roger Chillingworth‚ made her keep their marriage a
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To Whom It May Concern‚ This letter is written in an attempt to appeal my academic probation and allow me to receive financial aid so I can continue my college education. During 2007 and 2008 my grades were poor. The cause is no less than my own fault‚ but I believe the circumstances I faced led my focus away from my education. In the spring of 2007 my father suffered a heart attack. This event sent my world into a spiral. I continued school as best I could and helped my mother take care of
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