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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Best Friends and Enemy In our society‚ relationships between people are very important part in life. Goran Stojanoy once said‚ “Once should always take care when making a choice of a friend as the friends are the ones you pick by yourself.” Also‚ friends come and go‚ but with some special people they stay in our life forever. In life we spend approximately 30% of our time socializing with people‚ making friends is one of the process. It depends on the person who is trying to be friends with you
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should have a best friend. I am lucky enough to have two! There exists a popular phrase‚ “dog is mans best friend‚” and indeed my dog‚ Maxwell‚ is my best friend. Maxwell is a cuddly‚ 5 year-old cocker spaniel and poodle mixture‚ weighing in at roughly 20 pounds. In addition‚ a lovely lady by the name of Jenna Michelle also earns the “best friend” title in my life. Jenna is a 27 year-old goofy lady who has shown me solid friendship for the past three years. I spend a majority of my time with both
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Wilke English Comp.1 March 26‚ 2013 Best Friend vs Dogs Believe it or not‚ Friends and dogs have many similarities. They both make great companions and we here‚ they both play an important role in our life. The real subject I would like to point out is who’s actually a better friend? I believe man’s best friends are more true than their human counterpart because you can trust them. Try to question yourself‚ who’s
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Best friend becomes enemy. It was first day of summer. School almost finished. It was sunny and windy day. I was happy that school almost finished. My friend and I were sitting at the park. We were planning how to spend this long summer. George‚ my friend‚ gave me many plans for this summer but I didn’t agree with him. He was a lazy gay. His plan was: sleep till 11 a.m.‚ and then play video games till 5 p.m. and then go to sleep. He says that this must continue every day.
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Big Brother‚ Best Friend Oceania: a society where people are completely unified against the treachery of one Emmanuel Goldstein. In rejection of Goldstein‚ they fully accept Big Brother‚ their eternal guardian and savior. While citizens are strongly bound together by these shared views‚ little emotional connection exists between individuals. Isolation and alienation of is a tool used by the government to regulate emotions and thought of citizens. As a primary characteristic of dystopian literature
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superorganism‚ that is‚ rather than a plain old individual human being. It happened on March 7. That’s when I opened my e-mail to find a huge‚ processor-choking file of charts and raw data from a laboratory located at the BioFrontiers Institute at the University of Colorado‚ Boulder. As part of a new citizen-science initiative called the American Gut project‚ the lab sequenced my microbiome — that is‚ the genes not of “me‚” exactly‚ but of the several hundred microbial species with whom I share this
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convinced that there is nothing better than getting into my warm flannel pajamas after a long‚ cold‚ boring day at school. Walking through my front door knowing that they are waiting for my arrival‚ taking off those every-girl-has-to-have-them-skin-tight-pants and putting on loose stretchy flannel bottoms is better than an ice cold glass of lemonade on a sweltering hot summer day. Spotting that cute matching top and pulling it over my head informs me that I am ready for an all-you- can-eat
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always been man’s best friend and there are many reasons that this is true. Dogs are always loyal‚ offering unconditional love and protection. They make our lives healthier by convincing us to stay active‚ because they are always willing to play. It’s even proven that owning a pet‚ whether it’s a dog or cat can actually lower your blood pressure by keeping you calmer and happier. They can always manage to put a smile on your face‚ no matter what mood you’re in. The best things dogs have done
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Books Books are the best friend a person can have. For they are the kind of friends that are never disloyal. A person is never going to feel alone or bored in the presence of books. So‚ books can be read out of passion as a hobby or to gain knowledge and information. For that‚ some books are to be tasted‚ others to be swallowed; and some few to be chewed and digested. There are certain types of books which can only be tasted. To taste a book is just to have some sensations out
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