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STT315: Mathematical Statistics with Applications Department of Mathematics and Statistics, UNC Wilmington Dr. Cuixian Chen 1
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What is Statistics? collection or gathering of data displaying, analyzing, and summarizing data inferring information from data
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What are the differences b/w STT215 and STT315 STT 315 is more advanced in terms of abstract thinking STT 315 provides many basic and useful knowledge for advanced statistics classes, as well as classes in other subjects that use statistics. Actuaries? Data Science? Big Data? Biostatistics? Stt315 needs solid training in mathematics such as CALCULUS 1,and 2! Skills in derivatives and integrals including multiple integrals are REQUIRED! 3
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STT315 Challenges It is a very difficult class. Some of you may even find it harder than many other graduate statistics courses. Steep learning curve. Twisted with probability and Calculus-I/II. It has its realm of notations and ideas, which may be different from other Mathematical courses. Some students found out it has nowhere to set out for some probability problems. No pain, no gain…
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STT315 Learning Outcome We will cover the most fundamental backgrounds for Probability and Statistics. You will have solid foundation on Statistics and Probability. You will be well prepared for any advanced graduate level statistics/probability courses. You are ready to face any challenges on Actuary Exams Oh… graduate school, I am coming!
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DW Simpson 2011 Salary Survey Source: dwsimpson.com/salary
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DW Simpson 2011 Salary Survey Actuary Exam "Be An Actuary" Website (click here)Be An Actuary" Websiteclick here Salary survey for actuary (from DW Simpson) Salary survey for actuary Actuary Exam P and STT 315 Actuary Exam P and STT 315 Classes offered at UNCW to help you to prepare Actuary Exams.Past Exam Questions and Solutions Classes offered at UNCW to help you to prepare Actuary Exams.Past Exam Questions and Solutions Exam P/1 Sample Questions and Solutions Sample QuestionsSolutions MAT381, MAT468 for preparing first two actuary exams.
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Courses requirements for Data Science Biostatistics Analysis/Survival Analysis (STT520/420); Categorical Data Analysis (STT525/425); Linear/Multivariate Models and Regression Analysis (STT540/440); Design of Experiments and Analysis of Variance (STT511/411); Statistical Inference (STT566/466); Nonparametric Statistics (STT530/430); Additional: Probability, Longitudinal Analysis, Generalized Linear Model; Introduction to Statistical learning and data mining. STT520-420 8
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Typical Job duty of Biostatistician Duty of Biostatistician: Write/review Statistical Analysis Plan (SAP). Write/review statistical section of protocol including sample size calculation, develop randomization schedule, mock up table shells/listing shells, provide specifications to programmers. Quality control the table from SAS programmer, and review listings. Validate deliverables. STT520-420 9
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Typical Job duty of SAS programmer Duty for SAS programmer: Data validation: Data cleaning, Error checking. Build analysis database, based on the specifications from Biostatistician. Build table shells and listing shells for the Biostatistician to review and quality control. Require SAS Macro. STT520-420 10
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Contract Research Organization (CRO) CRO = Contract Research Organization Most projects are the clinical trials from large pharmaceutical company. Local CRO: PPD; Quintiles; INC Research, and so on… STT520-420 11
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Quick review of chapter 1 Sample mean : Sample variance : Sample SD (standard deviation) : Suppose that th observations in a sample are x 1,x 2,…,x n. The sample mean, denoted by is: The sample variance, denoted by s 2, is given by The sample standard deviation, denoted by s, is the positive square root of s 2, that is, The population mean is denoted by µ. The population sd is denoted by σ. HW: EX 1.10,1.11, 1.13 (refer to the observation in 1.12) 12
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13 Review STT215 Density Curves and Normal Distribution Definition, pg 56 Introduction to the Practice of Statistics, Sixth Edition © 2009 W.H. Freeman and Company
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Normal distributions e = 2.71828… The base of the natural logarithm π = pi = 3.14159… Normal – or Gaussian – distributions are a family of symmetrical, bell shaped density curves defined by a mean (mu) and a standard deviation (sigma) : N( ). xx
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mean µ = 64.5 standard deviation = 2.5 N(µ, ) = N(64.5, 2.5) All Normal curves N ) share 68-95-99.7 Rule Reminder: µ (mu) is the mean of the idealized curve, while x¯ is the mean of a sample. s (sigma) is the standard deviation of the idealized curve, while s is the s.d. of a sample. About 68% of all observations are within 1 standard deviation ( of the mean ( ). About 95% of all observations are within 2 of the mean . Almost all (99.7%) observations are within 3 of the mean. Inflection point
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Standard Normal distributions Empirical Rule: For a distribution of measurements that is approximately normal, it follows that the interval with end points About 68% of all observations are within 1 standard deviation ( of the mean ( ). About 95% of all observations are within 2 of the mean . Almost all (99.7%) observations are within 3 of the mean . N(0,1) => N(64.5, 2.5) Standardized height (no units)
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