STAT 360 Probability and Statistics. Fall 2012

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1 STAT 360 Probability and Statistics Fall ) General information: Crosslisted course offered as STAT 360, MATH 360 Semester: Fall 2012, Aug 20--Dec 07 Course name: Probability and Statistics Number of credits: 3 Course Prerequisite: MATH 172 or MATH 182 Section 1. Schedule Line Number (SLN): 29161, Lectures: TU,TH , Bldg & Room VUB 100 Section 2. SLN: 29163, Lectures: TU,TH , Bldg & Room VUB 100 2) Instructors Instructor: Nikolay Strigul Phone: Office Hours: M, W and by appointment Teaching Assistant: Ward, Jennifer Schmidt Office Hours: Monday and Tuesday ) Required textbook Probability & Statistics for Engineers & Scientists by R.E. Walpole, R.H. Myers, S.L. Myers, K. Ye 4) Course description STAT360 is a standard undergraduate course in probability and statistics for undergraduate students in sciences and engineering. This course covers basic concepts and methods in probability and statistics such as sample space, discrete and continuous random variables, probability distributions, introduction to the statistical inference, estimation, and statistics. Students will have weekly homework. There will be 2 quizzes and midterm and final exams. 5) Workload and grading Homework assignments: There will be weekly homework assignments. Exams: There will be midterm and final exams. Quizzes: There will be 2 quizzes. Grading: Homework assignments: 20 % Quizzes: 20 % Midterm: 25 % Final: 35 %

2 6) Learning Outcomes Graduates will have a basic understanding of probability reasoning required for a broad range of industrial and scientific applications; students will also have an elementary understanding of statistics. LO1 LO2 LO3 LO4 At the end of this course, students should be able to: Understand and apply for problem solving the following concepts: sample space, probability, conditional probability, dependent and independent events, and Bayes rule. Understand and employ the concept of random variables; use distribution and cumulative distribution of random variables, and calculate moments of functions of random variables. Use the concept of bivariate distributions to calculate basic two-variable statistics (covariance, correlation). Demonstrate in depth knowledge of the basic discrete (Binomial, Geometric, Negative Binomial, Hypergeometric, and Poisson) and continuous (Uniform, Normal, and Student t) distributions and apply these distributions to the standard problems from engineering and scientific Course topics (and dates) that address these learning outcomes are: 2 Sample space (8/23/2012) 3 Counting sample points (8/28/2012, 8/30/2012) 4 Probability (9/4/2012, 9/6/2012) 5 Conditional probability and independence (9/11/2012, 9/13/2012) This outcome will be evaluated primarily by: 2) Quiz 1 3) Midterm exam 4) Final exam 6 Random variables (9/20/2012) 2) Midterm exam 7 Joint probability distributions, independence 3) Final exam (9/25/2012, 9/27/2012) 8 Mathematical expectation (10/2/2012, 10/4/2012) 10 Means of linear combinations of random variables (10/11/2012) 11 Variances of functions of random variables (10/16/2012) 9 Covariance (10/9/2012) 13 Discrete probability distributions 1 (10/30/2012, 11/1/2012) 14 Discrete probability distributions 2 (11/6/2012, 11/8/2012) 15 Continuous probability distributions (11/15/2012) 16 Fundamental sampling distributions (11/20/2012, 11/22/2012) 2) Midterm exam 3) Final exam 2) Quiz 2 3) Final exam

3 LO5 LO6 practice. Use graphs, histograms and computer programs to visualize distributions of discrete and continuous random variables. Perform simple hypothesis tests, calculate point estimates and confidence intervals for a single population sample. (WSU Goal: Quantitative 6 Random variables (9/20/2012) 7 Joint probability distributions, independence (9/25/2012, 9/27/2012) 8 Mathematical expectation (10/2/2012, 10/4/2012) 13 Discrete probability distributions 1 (10/30/2012, 11/1/2012) 14 Discrete probability distributions 2 (11/6/2012, 11/8/2012) 15 Continuous probability distributions (11/15/2012) 16 Fundamental sampling distributions (11/20/2012, 11/22/2012) 17 Single sample (11/27/2012) 18 Statistical hypotheses (11/29/2012, 12/4/2012) 2) Final exam

4 7) Course outline Date Topic 21 T 1 Introduction to statistics and data analysis August 23 Th 2 Sample space 28 T 3 Counting sample points 30 Th 3 4 T 4 Probability 6 Th 4 11 T 5 Conditional probability and independence September 13 Th 5 18 T Quiz 1 20 Th 6 Random variables 25 T 7 Joint probability distributions, independence 27 Th 7 2 T 8 Mathematical expectation 4 Th 8 9 T 9 Covariance 11 Th 10 Means of linear combinations of random variables October 16 T 11 Variances of functions of random variables 18 Th 12 Chebyshev's Theorem 23 T Review 25 Th Midterm Exam 30 T 13 Discrete probability distributions 1 1 Th 13 6 T 14 Discrete probability distributions 2 8 Th T Quiz 2 November 15 Th 15 Continuous probability distributions 20 T 16 Fundamental sampling distributions 22 Th T 17 Single sample 29 Th 18 Statistical hypotheses December 4 T 18 6 Th Review Final exam

5 8) Course topics Topic 1. - Introduction to statistics and data analysis Sampling procedures Measures of location: the sample mean Measures of variability Discrete and continuous data Graphical methods and data descriptions Topic 2. - Sample space Sample space Events Complement of an event Intersection and union of events Disjoint events Venn diagrams Topic 3. - Counting sample points The multiplication rule Permutations Number of permutations of n distinct objects taken r at a time Number of permutations of n things of k kinds Number of ways of partitioning a set of n objects Number of combinations of n distinct objects taken r at a time Topic 4. - Probability Probability of an event Probability and relative frequency Additive rule for two events Partition of sample space Generalisation of additive rule for three events Topic 5. - Conditional probability and independence Conditional probability Independent events Multiplicative rules Bayes' formula Topic 6. - Random variables Concept of random variable Discrete probability distributions Continuous probability distributions Topic 7. - Joint probability distributions, statistical independence Joint probability distributions Marginal distributions Conditional distributions Statistical independence

6 Topic 8. - Mathematical expectation Mean of random variable Variance Standard deviation Topic 9. - Covariance Covariance Correlation coefficient Topic Means of linear combinations of random variables Expected value of a linear function of a random variable Expected value of the sum or difference of functions of a random variable Expected value of multiplication of two independent random variables Topic Variances of functions of random variables Variance of a linear function of a random variable Variance of a linear combination of two random variables Expected value and variance of non-linear functions of a random variable Linearization Topic Chebyshev's Theorem Chebyshev's Theorem Topic Discrete probability distributions 1 Discrete uniform distribution The Bernoulli process Binomial distribution Topic Discrete probability distributions 2 Hypergeometric distribution Negative binomial distribution Poisson process Topic Continuous probability distributions 1 Continuous uniform distribution Normal distribution Areas under the normal curve Applications of the normal distribution Topic Fundamental sampling distributions Random sampling Some important statistics Sampling distribution of means Sampling distribution of sample variances t-distribution Topic Single sample

7 Estimating the mean Standard error Prediction intervals Topic Statistical hypotheses Testing a statistical hypothesis P-values One- and two-tailed tests

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