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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In my perfect world‚ everyone is kind. Any girl who has ever snubbed another will come to the realisation that life is too precious to waste it with snide comments. Everyone who has every taken advantage of their beauty‚ will descend from their high horse and hold hands with those of our level. The words "fat" and "ugly" do not exist. In my perfect world‚ cancer is an illusion. Diabetics can eat all the chocolate they like without endangering themselves‚ the mentally ill will clear their minds‚
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Lina Abdo Sept. 18‚ 2012 Period 4A My Perfect College My perfect college has to have all of the things I want in it. It has to be a university with a great medical and health program. Also‚ it has to be located near a beach and city‚ and have plenty of school spirit. These attributes would make my dream college a perfect place to learn because it would be very connected campus-wide and be a fun and safe environment for students. A great medical program is essential for me because pharmacy
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Michigan Tech I woke up to my alarm beeping. I was anxious to get headed up to Michigan Tech for the week. I woke up my mom and then she drove me to Masyn’s house. Once we got there I loaded my stuff up into Masyn’s car and then we were on our way. Masyn and I arrived at Michigan Tech at around noon and then went to go get signed in. After I got my lanyard‚ I headed up to my room. I got there and realized that my name wasn’t hung up on my door. I went and told the counselor and he brought me
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Celeste Essel Mrs.Hurey English 10 9 September 2013 My Perfect Vacation A perfect vacation‚ in my opinion‚ would consist of a ocean nearby a lavish‚ roomy beach house‚ under a sunny blue sky. To add to this fantasy‚ a nice breeze would be perfect to make the palm tree leaves wave hello to me‚ as my hair sways in it’s subtle winds. A beach that is nearby is fundamental for so many reasons. One activity a person could do while walking along the shore is looking for sea shells‚ which
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A Perfect Life My daily morning routine leads me to realize one thing - my life is perfect. Every day when I wake up‚ I curse my alarm‚ stumble to the bathroom‚ and brush my teeth while I stare out the window. Sometimes I stand there too long‚ or at least longer than my sleepy body allows. Regardless‚ I enjoy this. Here I can meditate about everything that I do: breaking my pitching wedge in half in frustration after a poor round of golf or completing a plethora of schoolwork. However‚ only
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My Perfect Wedding Christmas Day is usually a holiday mainly observed to commemorate the birth of Jesus. For non Christianity followers it is a day to exchange gifts‚ decorate houses and for Santa Clause. For me‚ Christmas of two thousand eight changed my life forever. This is the day my now to be husband kneeling down on one knee‚ asked me to spend the rest of my life with him. His proposal was short sweet and sincere. Without a doubt I gracefully replied “Yes‚ I will.” With many new emotions
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The Perfect Boyfriend - College Essay When I describe the perfect boyfriend I could have‚ I think of one I already had. When I was a sophomore‚ I met a different kind of boy. One who was sweet‚ and warm and funny: different. He was a puzzle piece that didn’t fit the rest of the puzzle and just right for me. Before him‚ I always thought my first love was my first boyfriend‚ but no‚ this one was. The first thing I noticed was his dark chocolate brown eyes‚ and I was hooked. He had soft‚ floppy
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My Perfect Job My idea of the perfect job is one that will allow me to use the skills and knowledge I have gained‚ while also allowing some flexibility in my time‚ and keeping my interest. Having work that is financially rewarding goes without saying. I love working with computers‚ setting them up‚ fixing problems‚ doing upgrades‚ and teaching people to use them. I spend much of my free time doing this sort of work for friends and family. I have spent more Saturday’s than I can count answering
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No day is perfect as something always seems to go wrong. Little or big there is always a flaw. That is what I have always believed in and probably always will. Anyone that says something is perfect is either lying through their teeth or overlooking a bunch of things. Some days do come close though. Some days just are so wonderful they seem perfect. They seem like the best day you’ve ever had. That doesn’t mean they are but they do come very close. For me a nice summer day always is the start of
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