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
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
Premium English-language films The Devil Went Down to Georgia Hiking
1. A friend in need is a friend indeed. This famous saying holds true. A true friend never sees only your good days and good deeds but he stands by you even on the darkest day of your life. Ramu Rao studies in my class. We have been friends since class two. On many occasions when I would forget my lunch box at home‚ he has shared his tiffin with me. Once when I nearly fought with the class bully he saved me. He thought that no good would come from bad actions and to get good things in life one
Premium Friendship Virtue Interpersonal relationship
My Best Friend The year was a strange one‚ one that was beyond anything I had ever experienced before in my short 12 years on planet Earth. The Y2K scare had everyone running for water‚ food and power supplies in the beginning. I was leaving elementary school and life couldn’t be happier. Between the “summer Olympics”‚ my friends and I developed‚ the beautiful scents of the local woods‚ the ma and pa ice cream shop we went to in downtown Crete‚ Illinois‚ or the new addition of all of us reading
Premium Harry Potter
My friend has been such a delightful and influential person in my life. She is apologetic and leads me on the right path. My friend gives me helpful guidance when I feel disheartened or hurt at times and I am so grateful to have a true friend who will stand up for me‚ shield me‚ tell me I was wrong and show and heartening way to do the right thing in life and I appreciate her honesty and integrity toward me and my family. I feel as though my friend will always support me whether I’m right or wrong
Premium 2002 albums Carrie Underwood Shopping mall
Book is the Best Friend I’ve always imagined that Paradise will be a kind of library‚ says Jorge Luis Borges. “A true friend is your 2nd self”. This is my personal experience that‚ like human friends‚ books are our best companions. When I read a book‚ I feel like talking to my best friend. Every book I read moulds my strengths and shapes my personality. Book gives us education‚ knowledge and pleasure. Importance of reading books beggars description. Book is our great advisor because when we face
Premium Jorge Luis Borges Mind Consciousness
My Best Friend When we were in high school we do things to fit in with others‚ and to be able to say that you have at least experienced with things. Well‚ when I was in high school I got mixed up in the wrong crowd and started doing things that I am not so proud of. I was mixed up with people who used drugs and drank every day. This became such a routine thing for me that I dropped out of school after finishing my freshman year. I enrolled into GED classes but that didn’t work out because I was
Premium High school
My Friend Max By: Shane Droske FOREWORD By: Brittany Mineard Many people don’t recognize suicide as a major problem until it directly effects their lives. Many people also don’t connect suicide with the amount of deaths within the teenage population. In fact‚ teen suicide is a major cause of death among teens‚ being the third leading cause. According to the National Institute for Mental Health (NIMH)‚ about 8 out of every 100‚000 teenagers committed suicide in the year
Premium Suicide
Write an essay about my best friend The best friend who can share everything with you‚ you feel comfortable aroud your friend and the best friend is ready to help you when you have difficulty. I would like to introduce my best friend to all of you. He’s TINH. He’s 26 years old‚ he comes from Ninh Binh Province. Now‚ he is living in Long An Province. I have been knowing him when I was high school. He is a good-looking man. He has brown eyes‚ a straight nose and black hair‚ he is rather tall. I
Premium High school Friendship Family
Almost immediately after his release ‚ he hanged himself from the heating pipes in his room . Before committing suicide‚ Sergei Yesenin wrote a poem in his own blood. Goodbye‚ my friend‚ goodbye My love‚ you are in my heart. It was preordained we should part And be reunited by and by. Goodbye‚ my friend‚ without pens or words.: no handshake to endure. Let’s have no sadness — furrowed brow. There’s nothing new in dying now Though living is no newer. Death is inevitable.Death
Premium Poetry Suicide Rhyme