[major=AI | course_id=MAS291 | syllabus_id=13136 | semester=3 | combo=core | title=Statistics & Probability]
Course ID: MAS291
Title EN: Statistics & Probability
Title VI: Xác suất thống kê
Credits: 3.0
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)
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)
Course type: traditional
Decision: 932/QĐ-ĐHFPT dated 08/22/2025
Approved date: 2025-08-22
CLO1: 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.
[1] category=Assignment; type=on-going; weight=20.0; duration=3 hours; question_type=LO1, LO2, LO3, LO4, LO5, LO6; grading_guide=Assignment 1 covers Chapters 1, 2, 3 ; Assignment 2 covers Chapters 4, 6, 7; completion_criteria=; clos=>0
[2] category=Computer Project; type=on-going; weight=15.0; duration=5 hours; question_type=LO7, LO8, LO9; grading_guide=Computer Project covers Chapter 8, 9, 10, 11; completion_criteria=; clos=>0
[3] category=Progress Test; type=on-going; weight=30.0; duration=30'; question_type=All LOs; grading_guide=Chapters introduced; completion_criteria=; clos=>0
[4] category=Final exam; type=Final exam; weight=35.0; duration=60'; question_type=; grading_guide=All studied chapters
3-10 questions/each.
More than 70% new questions (for the current semester);; completion_criteria=Every on-going assessment component > 0, Final Result >=5 & Final Exam Score >=4; clos=4
[1] desc=Montgomery D.C. & Runger G.C., Applied Statistics and Probability for Engineers; author=John Wiley & Sons.; publisher=Wiley; edition=4th/5th/6th/7th ed.; isbn=9781119718871; main=True; online=True; note=7th ed. ISBN: 9781119718871
[2] desc=Powerpoint slides (PP).; author=; publisher=; edition=; isbn=; main=; online=; note=
[3] desc=Computerized tools (for example Excel and DDXL add-ons) (CT); author=; publisher=; edition=; isbn=; main=; online=; note=
[4] desc=Elementary Statistics Using Excel, 3/E,; author=Mario F. Triola; publisher=Addison-Wesley; edition=3rd; isbn=0321365135; main=; online=; note=
Session 1: The Roles of Statistics in Engineering
1.1 The Engineering Method and Statistical Thinking
1.2 Collecting Engineering Data
Topic: Offline; Teaching type: LO1; LO: IT
ITU: Textbook Chapter 1
Download: Exercises Chapter 1
Assignment 1

Session 2: The Roles of Statistics in Engineering
1.3 Mechanistic and Empirical Models
1.4 Probability and Probability Models
Topic: Offline; Teaching type: LO1; LO: IT
ITU: Textbook Chapter 1
Materials: MAS291
Download: Exercises Chapter 1
Assignment 1

Session 3: Probability
2.1 Sample Spaces and Events
Topic: Offline; Teaching type: LO2; LO: IT
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1

Session 4: Probability
2.2 Interpretations of Probability
2.3 Addition Rules
Topic: Offline; Teaching type: LO2; LO: IT
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1
CLO2: 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.
Session 1: Probability
2.4 Conditional Probability
Topic: Offline; Teaching type: LO2; LO: TU
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1

Session 2: Probability
2.5 Multiplication and Total Probability Rules
2.6 Independence
Topic: Offline; Teaching type: LO2; LO: TU
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1

Session 3: Probability
2.7 Bayes' Theorem
Topic: Offline; Teaching type: LO2; LO: ITU
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1

Session 4: Probability
2.8 Random Variables
Topic: Offline; Teaching type: LO2; LO: ITU
ITU: Textbook Chapter 2
Download: Exercises Chapter 2
Assignment 1
CLO3: 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.
Session 1: Discrete Random Variables and Probability Distribution
3.1 Discrete Random Variables
Topic: Offline; Teaching type: LO3; LO: ITU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 2: Discrete Random Variables and Probability Distribution
3.2 Probability Distributions and Probability Mass Functions
Topic: Offline; Teaching type: LO3; LO: ITU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 3: Discrete Random Variables and Probability Distribution
3.3 Cumulative Distribution Functions
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 4: Discrete Random Variables and Probability Distribution
3.4 Mean and Variance of a Discrete Random Varibale
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1
CLO4: 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.
Session 1: Discrete Random Variables and Probability Distribution
3.5 Discrete Uniform Distribution
3.6 Binomial Distribution
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 2: Discrete Random Variables and Probability Distribution
3.7 Geometric and Negative Binomial Distributions
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 3: Discrete Random Variables and Probability Distribution
3.8 Hypergeometric Distribution
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1

Session 4: Discrete Random Variables and Probability Distribution
3.9 Poisson Distribution
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 3
Download: Exercises Chapter 3
Assignment 1
CLO5: 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.
Session 1: Solve questions and problems for Chapters 1 - 3
Topic: Offline; Teaching type: LO1, LO2, LO3; LO: 
ITU: Textbook Chapters 1 - 3
Download: Exercises Chapters 1 - 3
Assignment 1

Session 2: Progress Test 1
Topic: Offline; Teaching type: LO1, LO2, LO3; LO: 
ITU: 

Session 3: Continuous Random Variables and Probability Distribution
4.1 Continuous Random Variables
4.2 Probability Distributions and Probability Density Functions
Topic: Offline; Teaching type: LO4; LO: ITU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 4: Continuous Random Variables and Probability Distribution
4.3 Cumulative Distribution Functions
Topic: Offline; Teaching type: LO4; LO: ITU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2
CLO6: 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.
Session 1: Continuous Random Variables and Probability Distribution
4.4 Mean and Variance of a Continuous Random Variable
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 2: Continuous Random Variables and Probability Distribution
4.5 Continuous Uniform Distribution
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 3: Continuous Random Variables and Probability Distribution
4.6 Normal Distribution
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 4: Continuous Random Variables and Probability Distribution
4.6 Normal Distribution (Cont.)
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2
CLO7: 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.
Session 1: Continuous Random Variables and Probability Distribution
4.7 Normal Approximation to the Binomial and Poisson Distributions
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 2: Continuous Random Variables and Probability Distribution
4.8 Exponential Distribution
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
Assignment 2

Session 3: Descriptive Statistics
6.1 Numerical Summaries
Topic: Offline; Teaching type: LO5; LO: IT
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
Assignment 2

Session 4: Descriptive Statistics
6.2 Stem-and-Leaf Diagrams
6.3 Frequency Distributions and Histograms
Topic: Offline; Teaching type: LO5; LO: IT
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
Assignment 2
CLO8: 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.
Session 1: Descriptive Statistics
6.4 Box Plots
Topic: Offline; Teaching type: LO5; LO: IT
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
Assignment 2

Session 2: Descriptive Statistics
6.5 Time Sequence Plots
Topic: Offline; Teaching type: LO5; LO: IT
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
Assignment 2

Session 3: Sampling Distributions and Point Estimation of Paramaters
7.1 Point Estimation
Topic: Offline; Teaching type: LO6; LO: I
ITU: Textbook Chapter 7
Download: Exercises Chapter 7
Assignment 2

Session 4: Sampling Distributions and Point Estimation of Paramaters
7.2 Sampling Distributions and the Central Limit Theorem
Topic: Offline; Teaching type: LO6; LO: I
ITU: Textbook Chapter 7
Download: Exercises Chapter 7
Assignment 2
CLO9: 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.
Session 1: Solve questions and problems for Chapters 4, 6, and 7
Topic: Offline; Teaching type: LO4, LO5, LO6; LO: 
ITU: Textbook Chapters 4, 6, and 7
Download: Exercises Chapters 4, 6, and 7
Assignment 2

Session 2: Progress Test 2
Topic: Offline; Teaching type: LO4, LO5, LO6; LO: 
ITU: 

Session 3: Statistical Intervals for a Single Sample
8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project

Session 4: Statistical Intervals for a Single Sample
8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known (Cont.)
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project
Session 1: Statistical Intervals for a Single Sample
8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project

Session 2: Statistical Intervals for a Single Sample
8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown (Cont.)
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project

Session 3: Statistical Intervals for a Single Sample
8.4 Large-Sample Confidence Interval for a Population Proportion
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project

Session 4: Statistical Intervals for a Single Sample
8.4 Large-Sample Confidence Interval for a Population Proportion (Cont.)
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 8
Download: Exercises Chapter 8
Project
Session 1: Test of Hypotheses for a Single Sample
9.1 Hypothesis Testing
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project

Session 2: Test of Hypotheses for a Single Sample
9.1 Hypothesis Testing (Cont.)
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project

Session 3: Test of Hypotheses for a Single Sample
9.2 Tests on the Mean of a Normal Distribution, Variance Known
Topic: Offline; Teaching type: LO8; LO: IT
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project

Session 4: Test of Hypotheses for a Single Sample
9.2 Tests on the Mean of a Normal Distribution, Variance Known (Cont.)
Topic: Offline; Teaching type: LO8; LO: IT
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project
Session 1: Test of Hypotheses for a Single Sample
9.3 Tests on the Mean of a Normal Distribution, Variance Unknown
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project

Session 2: Test of Hypotheses for a Single Sample
9.5 Tests on a Population Proportion
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook Chapter 9
Download: Exercises Chapter 9
Project

Session 3: Statistical Inference for Two Samples
10.1 Inference on the Difference in Means of Two Normal Distributions, Variance Known
Topic: Offline; Teaching type: LO7,LO8; LO: TU
ITU: Textbook Chapter 10
Download: Exercises Chapter 10
Project

Session 4: Statistical Inference for Two Samples
10.2 Inference on the Difference in Means of Two Normal Distributions, Variance Unknown
Topic: Offline; Teaching type: LO7,LO8; LO: TU
ITU: Textbook Chapter 10
Download: Exercises Chapter 10
Project
Session 1: Statistical Inference for Two Samples
10.6 Inference on the Two Proportions
Topic: Offline; Teaching type: LO7,LO8; LO: TU
ITU: Textbook Chapter 10
Download: Exercises Chapter 10
Project

Session 2: Statistical Inference for Two Samples
10.6 Inference on the Two Proportions (Cont.)
Topic: Offline; Teaching type: LO7,LO8; LO: TU
ITU: Textbook Chapter 10
Download: Exercises Chapter 10
Project

Session 3: Simple Linear Regression and Correlation
11.1 Empirical Models
Topic: Offline; Teaching type: LO9; LO: I
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project

Session 4: Simple Linear Regression and Correlation
11.2 Simple Linear Regression
Topic: Offline; Teaching type: LO9; LO: I
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project
Session 1: Simple Linear Regression and Correlation
11.3 Properties of the Least Squares Estimators
Topic: Offline; Teaching type: LO9; LO: ITU
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project

Session 2: Simple Linear Regression and Correlation
11.4 Hypothesis Tests in Simple Linear Regression
Topic: Offline; Teaching type: LO9; LO: ITU
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project

Session 3: Simple Linear Regression and Correlation
11.8 Correlation
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project

Session 4: Simple Linear Regression and Correlation
11.8 Correlation (Cont.)
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 11
Download: Exercises Chapter 11
Project
Session 1: Project presentation
Topic: Offline; Teaching type: LO7, LO8, LO9; LO: U
ITU: 
Download: Project

Session 2: Project presentation (Cont.)
Topic: Offline; Teaching type: LO7, LO8, LO9; LO: U
ITU: 
Download: Project

Session 3: Project presentation (Cont.)
Topic: Offline; Teaching type: LO7, LO8, LO9; LO: U
ITU: 
Download: Project

Session 4: Progress Test 3
Topic: Offline; Teaching type: LO7, LO8, LO9; LO: U
ITU: