Statistics & Probability (MAS291)
Vietnamese title: Xác suất thống kê
Credits: 3
Prerequisites: MAE101 or MAC101

Description:
Upon finishing the course, students must acquire:
1. the following knowledge:(ABET a1)
• The fundamental principles of probability and their applications
• The frequently used probability distributions.
• The basics of descriptive statistics
• The inferences of statistics: parameter estimations, hypothesis testing, regressions & correlations.
2. the following skills: (ABET a2)
• Recognize simple statistical models and applied them to solve engineering problems.
• Use at least one statistical software (Excel, Maxima) for problem solving.
• Self-study skill. (ABET i)

Learning outcomes:
Discuss the roles of statistics in engineering LO1.1 Explain the types of reasoning of statistical inference; distinguish mechanistic models and empirical models, statistic and parameter, sample and population. LO1.2 Describe the different methods that engineers use to collect data.
Identify sample spaces and events, and use basic rules to calculate the probability of an event LO2.1 Describe the sample space and events of an experiment; distinguish continuous and discrete sample spaces; perform operations on events. LO2.2 Calculate the probability of an event in a discrete sample space; use addition and complementary rules to find probabilities. LO2.3 Calculate conditional probabilities; use multiplication rule, total probability rule and Bayes theorem to find probabilities. LO2.4 Determine if two events are independent; use independence to find probabilities. LO2.5 Recognize a random variable; distinguish continuous and discrete random variables.
Describe the probability distribution and calculate the mean and variance of a discrete random variable LO3.1 Describe a discrete random variable; check if a function is a probability mass function and use it to calculate probability; find the cumulative distribution function of a discrete random variable. LO3.2 Compute the mean and variance of a discrete random variable. LO3.3 Determine the probability, mean and variance of uniform, binomial, geometric and negative binomial, hypergeometric and Poisson distributions.
Describe the probability distribution and calculate the mean and variance of a continuous random variable LO4.1 Describe a continuous random variable; check if a function is a probability density function and use it to calculate probability; find the cumulative distribution function of a continuous random variable. LO4.2 Compute the mean and variance of a continuous random variables LO4.3 Apply the formulas of continuous uniform distribution and exponential distribution to solve problems. LO4.4 Manipulate probabilities of a standard normal distribution using Excel or table of data; standardize a normal distribution. LO4.5 Use normal distribution to approximate binomial and Poisson distributions.
Describe data using numerical summaries and visual displays LO5.1 Find numeric summaries of data; describe data using stem-and-leaf diagrams, frequency distributions, histograms, time series plots. LO5.2 Determine quartiles and construct the box plot for a data; identify outliers.
Discuss sampling distributions and use the Central Limit Theorem to analyze sampling distribution of the means LO6.1 Discuss sampling distributions; find the point estimation of a parameter. LO6.2 Apply Central Limit Theorem to calculate probabilities regarding the sampling distribution of the means.
Construct confidence intervals for a population parameter/difference of population parameters LO7.1 Construct a confidence interval for the population mean/difference of two population means and interpret its meaning; determine the size of the sample to improve the estimation. LO7.2 Construct a confidence interval for the population proportion/difference of two population pproportions and interpret its meaning; determine the size of the sample to improve the estimation.
Verify a claim about a population parameter/difference of population parameters using hypothesis testing LO8.1 Formulate the two hypotheses; identify critical values, test statistic and compute P-value for a test of hypotheses on population mean/difference of two population means LO8.2 Formulate the two hypotheses; identify critical values, test statistic and compute P-value for a test of hypotheses on population proportion/difference of two population proportions LO8.3 Identify type of errors in testing hypotheses.
Construct a simple linear regression model LO9.1 Compute various sums of squares for a set of data pairs. LO9.2 Determine the equation of linear regression and the correlation coefficient; use linear regression to predict future values. LO9.3 Perform a hypothesis test in simple linear regression; test the significance of regression using t-test.

Student tasks:
Students must attend at least 80% of contact hours in order to be
accepted to the final examination.

Tools:
- Internet
- Computerized tools (for example Excel and DDXL add-ons) (CT)

Materials:
description: Montgomery D.C. & Runger G.C., Applied Statistics and Probability for Engineers
author: John Wiley & Sons.
publisher: Wiley
published_date: 2006
edition: 4th/5th/6th/7th ed.
isbn: 9781119718871
note: 7th ed. ISBN: 9781119718871
description: Powerpoint slides (PP).
description: Computerized tools (for example Excel and DDXL add-ons) (CT)
description: Elementary Statistics Using Excel, 3/E,
author: Mario F. Triola
publisher: Addison-Wesley
published_date: 200
edition: 3rd
isbn: 0321365135

Assessments:
category: Assignment
type: on-going
weight: 20.0
duration: 3 hours
question_type: LO1, LO2, LO3, LO4, LO5, LO6
no_question: OP1: Open // OP2: (For Constructivism Approach only): Follow lecturer's proposal
knowledge_and_skill: 5--10
grading_guide: Assignment 1 covers Chapters 1, 2, 3 ; Assignment 2 covers Chapters 4, 6, 7
note: OP1: Each assignment is divided into two parts: the take-home component counts for no more than 50% of the total grade, and the in-class component counts for at least 50% (this may take the form of a presentation, essay, problem-solving, etc.).
OP2: (For Constructivism Approach only): Follow lecturer's proposal
category: Computer Project
type: on-going
weight: 15.0
duration: 5 hours
question_type: LO7, LO8, LO9
no_question: OP1: Open // OP2: (For Constructivism Approach only): Follow lecturer's proposal
grading_guide: Computer Project covers Chapter 8, 9, 10, 11
note: OP1: Groups of students are required to collect secondary data (topics may be suggested by instructor), form their own questions, and apply learned knowledge and methods of inferential statistics to analyze data and make conclusions about the populations.
Groups are expected to use a statistical software to perform the analysis and present their results to other groups in class.
The work (slides, source files, etc.) accounts for up to 50% of the grade, while presentation skills and the ability to answer questions account for at least 50%.
OP2: (For Constructivism Approach only): Follow lecturer's proposal
category: Progress Test
type: on-going
weight: 30.0
duration: 30'
question_type: All LOs
no_question: OP1: MC or a suitable format // OP2: (For Constructivism Approach only): Follow lecturer's proposal
knowledge_and_skill: 15
grading_guide: Chapters introduced
note: OP1: by instructor, and by
suitable means (computer, paper, oral...)
OP2: (For Constructivism Approach only): Follow lecturer's proposal
category: Final exam
type: Final exam
weight: 35.0
duration: 60'
no_question: Computer gradable
knowledge_and_skill: 50
grading_guide: All studied chapters
3-10 questions/each.
More than 70% new questions (for the current semester);
note: by Exam Board

Schedule:
session: The Roles of Statistics in Engineering
1.1 The Engineering Method and Statistical Thinking
1.2 Collecting Engineering Data
learning_outcomes: IT
session: The Roles of Statistics in Engineering
1.3 Mechanistic and Empirical Models
1.4 Probability and Probability Models
learning_outcomes: IT
materials: MAS291
session: Probability
2.1 Sample Spaces and Events
learning_outcomes: IT
session: Probability
2.2 Interpretations of Probability
2.3 Addition Rules
learning_outcomes: IT
session: Probability
2.4 Conditional Probability
learning_outcomes: TU
session: Probability
2.5 Multiplication and Total Probability Rules
2.6 Independence
learning_outcomes: TU
session: Probability
2.7 Bayes' Theorem
learning_outcomes: ITU
session: Probability
2.8 Random Variables
learning_outcomes: ITU
session: Discrete Random Variables and Probability Distribution
3.1 Discrete Random Variables
learning_outcomes: ITU
session: Discrete Random Variables and Probability Distribution
3.2 Probability Distributions and Probability Mass Functions
learning_outcomes: ITU
session: Discrete Random Variables and Probability Distribution
3.3 Cumulative Distribution Functions
learning_outcomes: TU
session: Discrete Random Variables and Probability Distribution
3.4 Mean and Variance of a Discrete Random Varibale
learning_outcomes: TU
session: Discrete Random Variables and Probability Distribution
3.5 Discrete Uniform Distribution
3.6 Binomial Distribution
learning_outcomes: TU
session: Discrete Random Variables and Probability Distribution
3.7 Geometric and Negative Binomial Distributions
learning_outcomes: TU
session: Discrete Random Variables and Probability Distribution
3.8 Hypergeometric Distribution
learning_outcomes: TU
session: Discrete Random Variables and Probability Distribution
3.9 Poisson Distribution
learning_outcomes: TU
session: Solve questions and problems for Chapters 1 - 3
session: Progress Test 1
session: Continuous Random Variables and Probability Distribution
4.1 Continuous Random Variables
4.2 Probability Distributions and Probability Density Functions
learning_outcomes: ITU
session: Continuous Random Variables and Probability Distribution
4.3 Cumulative Distribution Functions
learning_outcomes: ITU
session: Continuous Random Variables and Probability Distribution
4.4 Mean and Variance of a Continuous Random Variable
learning_outcomes: TU
session: Continuous Random Variables and Probability Distribution
4.5 Continuous Uniform Distribution
learning_outcomes: TU
session: Continuous Random Variables and Probability Distribution
4.6 Normal Distribution
learning_outcomes: TU
session: Continuous Random Variables and Probability Distribution
4.6 Normal Distribution (Cont.)
learning_outcomes: TU
session: Continuous Random Variables and Probability Distribution
4.7 Normal Approximation to the Binomial and Poisson Distributions
learning_outcomes: TU
session: Continuous Random Variables and Probability Distribution
4.8 Exponential Distribution
learning_outcomes: TU
session: Descriptive Statistics
6.1 Numerical Summaries
learning_outcomes: IT
session: Descriptive Statistics
6.2 Stem-and-Leaf Diagrams
6.3 Frequency Distributions and Histograms
learning_outcomes: IT
session: Descriptive Statistics
6.4 Box Plots
learning_outcomes: IT
session: Descriptive Statistics
6.5 Time Sequence Plots
learning_outcomes: IT
session: Sampling Distributions and Point Estimation of Paramaters
7.1 Point Estimation
learning_outcomes: I
session: Sampling Distributions and Point Estimation of Paramaters
7.2 Sampling Distributions and the Central Limit Theorem
learning_outcomes: I
session: Solve questions and problems for Chapters 4, 6, and 7
session: Progress Test 2
session: Statistical Intervals for a Single Sample
8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known
learning_outcomes: TU
session: Statistical Intervals for a Single Sample
8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known (Cont.)
learning_outcomes: TU
session: Statistical Intervals for a Single Sample
8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown
learning_outcomes: TU
session: Statistical Intervals for a Single Sample
8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown (Cont.)
learning_outcomes: TU
session: Statistical Intervals for a Single Sample
8.4 Large-Sample Confidence Interval for a Population Proportion
learning_outcomes: TU
session: Statistical Intervals for a Single Sample
8.4 Large-Sample Confidence Interval for a Population Proportion (Cont.)
learning_outcomes: TU
session: Test of Hypotheses for a Single Sample
9.1 Hypothesis Testing
learning_outcomes: TU
session: Test of Hypotheses for a Single Sample
9.1 Hypothesis Testing (Cont.)
learning_outcomes: TU
session: Test of Hypotheses for a Single Sample
9.2 Tests on the Mean of a Normal Distribution, Variance Known
learning_outcomes: IT
session: Test of Hypotheses for a Single Sample
9.2 Tests on the Mean of a Normal Distribution, Variance Known (Cont.)
learning_outcomes: IT
session: Test of Hypotheses for a Single Sample
9.3 Tests on the Mean of a Normal Distribution, Variance Unknown
learning_outcomes: TU
session: Test of Hypotheses for a Single Sample
9.5 Tests on a Population Proportion
learning_outcomes: TU
session: Statistical Inference for Two Samples
10.1 Inference on the Difference in Means of Two Normal Distributions, Variance Known
learning_outcomes: TU
session: Statistical Inference for Two Samples
10.2 Inference on the Difference in Means of Two Normal Distributions, Variance Unknown
learning_outcomes: TU
session: Statistical Inference for Two Samples
10.6 Inference on the Two Proportions
learning_outcomes: TU
session: Statistical Inference for Two Samples
10.6 Inference on the Two Proportions (Cont.)
learning_outcomes: TU
session: Simple Linear Regression and Correlation
11.1 Empirical Models
learning_outcomes: I
session: Simple Linear Regression and Correlation
11.2 Simple Linear Regression
learning_outcomes: I
session: Simple Linear Regression and Correlation
11.3 Properties of the Least Squares Estimators
learning_outcomes: ITU
session: Simple Linear Regression and Correlation
11.4 Hypothesis Tests in Simple Linear Regression
learning_outcomes: ITU
session: Simple Linear Regression and Correlation
11.8 Correlation
learning_outcomes: TU
session: Simple Linear Regression and Correlation
11.8 Correlation (Cont.)
learning_outcomes: TU
session: Project presentation
learning_outcomes: U
session: Project presentation (Cont.)
learning_outcomes: U
session: Project presentation (Cont.)
learning_outcomes: U
session: Progress Test 3
learning_outcomes: U