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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Leadership Assignment 5 Sarah Kamal 09-4714 ------------------------------------------------- 26th November 2012 Question 1: Was the research program a group or a team? If a team‚ what kind of a team was it? At first‚ before the assignment of a formal leader‚ it was a self-directed team on a whole of groups of people. It was a team because it was not inhibited by organizational boundaries. It was specifically formulated for a purpose and vision that was to develop a technique for large-scale
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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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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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Our Food is our Choice Genetically modified foods or GMOs (genetically modified organisms) resulted from “genetic engineering where scientists alter the genes of plant and animal DNAs for the desired specific traits” (Ackerman). In this case‚ GMOs have changes in their genomes and we cannot certainly tell how these changes can affect the consumers especially their health. In fact‚ according to Environment Canada‚ “Canada is the third largest producer of genetically modified organisms (GMOs) in
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sizes and have spectacular shapes (1). Bacteria are present in most habitats on the planet‚ growing in soil‚ water‚ acidic hot springs‚ radioactive waste‚ and deep in the Earth’s crust‚ as well as in organic matter and the live bodies of plants and animals (2). Bacteria is mostly thought of as a pathogen‚ while it is true that bacteria are responsible for a large number of human diseases‚ they are also very beneficial to humans. Some of the benefits include the symbiotic relationship they have with
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responsibilities. These responsibilities consists of responsibility as a servant of God‚ as a student (ourself)‚ as a child‚ and as a citizen. The first is responsibility as a servant of God. Have we run our duty as religious people? Many of us who are academically capable‚ fulfilled in terms of material but our soul is empty because it is not touched by religious values. For you‚ students‚ perform the obligation as a people‚ not to ask or complain but do your duty as a servant. Don’t just closer to Him when
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Woman’s best friend. 44% of Americans own a dog. I have owned three dogs in my lifetime; three in which I no longer own. Some say a dog is a man’s best friend‚ but to me‚ a dog is a woman’s best friend too. A dog is not just a friend though; it is part of the family. I have loved all of my dogs the same‚ but differently. Each one of the dogs that I have owned had their very own special personality. Each dog meant something different to me; I had my first dog (Sammy)‚ my best friend (Daisy)‚ and
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