Almost sure central limit theorem
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Almost sure central limit theorem
MINISTRY OF EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICSPHAM NGOC QƯYNH HUONGALMOST SURE CENTRAL LIMIT THEOREMBACHELO Almost sure central limit theorem OR THESISHanoi. 2019MINISTRY O1 EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT DE MATHEMATICSPHAM NGOC QUYN11 HUONGALMOST SURE CENTRAL LIMIT THEOREMSpeciality: Applied Mat lunaticsBACHELOR THESISSupervisor: PhD. Pham Viet HungHanoi. 2019ConfirmationThis dissertation has been written Almost sure central limit theorem on the basis of my research project carried at Hanoi Pedagogical University 2, under the supervision of Phi). Pham Viet Hung. The manuscript has neverAlmost sure central limit theorem
been published by others.The authorPham Ngoc Quynh HuongAcknowledgmentFirst anti foremost, my heartfelt, goes to my admirable supervisor, Mr. Pham ViMINISTRY OF EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICSPHAM NGOC QƯYNH HUONGALMOST SURE CENTRAL LIMIT THEOREMBACHELO Almost sure central limit theorem e completion of this study would not have been possible without his expert advice, close attention and unswerving guidance.Secondly, I am keen on expressing my deep gratitude for my family for encouraging me to continue this thesis. I owe my special thanks to my parents for their emotional anti mate Almost sure central limit theorem rial sacrifices as well as their understanding and unconditional support.Finally, 1 own my thanks to many people who helped me and encouraged me durinAlmost sure central limit theorem
g my work. My special thanks to Mr. Nguyen Phuong Dong (Hanoi Pedagogical University No.2) for his guidance on drawing up my work. 1 am specially thanMINISTRY OF EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICSPHAM NGOC QƯYNH HUONGALMOST SURE CENTRAL LIMIT THEOREMBACHELO Almost sure central limit theorem .1.Probability Space .................................................... 31.2.Random Variables...................................................... 41.2.1.Definition..................................................... 41.2.2.Distribution functions.................................. 41.2.3.Expectat Almost sure central limit theorem ion.................................................... 61.2.4.Variance....................................................... 81.2.5.Examples........Almost sure central limit theorem
............................................... 91.2.6.Some inequalities............................................. 13MINISTRY OF EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICSPHAM NGOC QƯYNH HUONGALMOST SURE CENTRAL LIMIT THEOREMBACHELOMINISTRY OF EDUCATION AND TRAININGHANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICSPHAM NGOC QƯYNH HUONGALMOST SURE CENTRAL LIMIT THEOREMBACHELOGọi ngay
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