Course Title | Probability & Statistics | ||
Course Code | MH2814 | ||
Offered | Study Year 2, Semester 1 | ||
Course Coordinators | Yeo Kwee Poo (Asst Prof) | kweepoo@ntu.edu.sg | 6513-7456 |
Chan Song Heng (Assoc Prof) | chansh@ntu.edu.sg | 6513 7453 | |
Pre-requisites | MH1810 OR MT1001 | ||
Mutually exclusive | MT2001, CV2001, CV2018, HE1005, MH2500 | ||
AU | 3 | ||
Contact hours | Lectures: 26, Tutorials: 12 | ||
Approved for delivery from | AY 2020/21 semester 1 | ||
Last revised | 29 May 2020, 08:56 |
Uncertainties are unavoidable in the design and planning of engineering system. Therefore, engineering analysis should include probability and statistics to evaluate the significance of uncertainty on system performance and design. This course provides the basics of probability and statistical concepts in terms that are more easily understood by engineering students. We present probability and statistical concepts through problems that are meaningful to engineering science. This course should motivate the recognition of the significant roles of the relevance mathematical concepts in engineering.
Upon successfully completing this course, you should be able to:
Topic 1: Basic Probability Theory: • Sample space, Events, Counting Sample Points, Permutations & Combinations. • Probability, Equally Likely Outcomes, Not Equally Likely outcomes, Useful Rules • Conditional Probability, Independent Events, Partition, Bayes’ Rule
Topic 2: Random Variables & Probability Distribution: • Random Variables (RV), Discrete Random variables, Probability Mass Distribution, Cumulative Probability Distribution • Bernoulli Distribution and Binomial Distribution • Continuous Random variables, Probability Density Function, Cumulative Distribution Function
Topic 3: Expectation & Variance : • Expectation of Discrete & Continuous RVs, Expectation of general RV, Useful Properties of Expectation, Variance & Properties
Topic 4: Joint Distribution : • Joint Probability Distribution & Marginal distribution (discrete RVs), Joint Probability Distribution & Marginal distribution (continuous RVs), Expectation E[g(X,Y)] • Conditional Probability Distribution, (Statistically) Independent RV. Variance, Covariance, Correlation coefficients, Useful Results
Topic 5: Special Discrete Probability Distributions : • Binomial, Geometric (return period), Poisson Distribution, Poisson Approximation
Topic 6: Normal Distribution : • Normal Distribution, Standard Normal Distribution (introduction) • Standard Normal Distribution, Mean & Variance (Proofs excluded) • Applications: Problems, Approximation of Binomial Distribution
Topic 7: Statistics: • Population & Parameters, Samples & Sample Statistics
Topic 8: Sampling Distribution and Estimation : • Random Sampling, Sampling Distribution, Distribution of Sample Mean, Central Limit Theorem • Unbiased Estimator of variance, chi-sq-distribution, Samples with Unknown Population Variance, t-distribution • Sampling Distribution of Difference between two Means
Topic 9 Confidence Interva: l • Confidence Intervals (introduction), Known/Unknown Variance, Large/Small Sample • Confidence Intervals (1-sided, 2-sided Confidence interval), Error, Size, Prediction Interval • 2-Population: confidence Interval, Small Size Unknown Variance
Topic 10: Hypothesis Testing: • Introduction, Type-1, Type-2 Error • Hypothesis Testing for Population Mean (1-population), Power, p-value • Hypothesis Testing for Difference between Population Means
Topic 11 Simple Linear Regression: • Linear Regression & Transformation • Estimation of Regression Parameters • Confidence Interval for Parameters in Linear Regression
Component | Course ILOs tested | EAB Graduate Attributes tested | Weighting | Team / Individual | Assessment Rubrics |
---|---|---|---|---|---|
Continuous Assessment | |||||
Mid-semester Quiz | |||||
Short Answer Questions 1 | 1, 2, 3, 4, 5, 6 | a, b, h, i, j, l | 20 | individual | See Appendix for rubric |
Short Answer Questions 2 | 7, 8, 9, 10 | a, b, h, i, j, l | 20 | individual | See Appendix for rubric |
Examination (2 hours) | |||||
Short Answer Questions | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 | a, b, h, i, j, l | 60 | individual | See Appendix for rubric |
Total | 100% |
Category | Core | ||||||||||||
EAB's 12 Graduate Attributes* | |||||||||||||
| |||||||||||||
Overall statement | |||||||||||||
Uncertainties are unavoidable in the design and planning of engineering system. Therefore, engineering analysis should include probability and statistics to evaluate the significance of uncertainty on system performance and design. This course provides the basics of probability and statistical concepts in terms that are more easily understood by engineering students. We present probability and statistical concepts through problems that are meaningful to engineering science. This course should motivate the recognition of the significant roles of the relevance mathematical concepts in engineering. | |||||||||||||
Course Student Learning Outcomes | EAB Graduate Attributes | ||||||||||||
1 | Use the techniques of permutations and combination to calculate the probability of the occurrence of an event | a, b, h, i, j, l | |||||||||||
2 | Apply Bayes’ rule to compute conditional probability and identify independent events | a, b, h, i, j, l | |||||||||||
3 | State the definition of a random variable (RV), tabulate its probability mass function or density function, and be able to compute its expectation and variance | a, b, h, i, j, l | |||||||||||
4 | Recognize a joint probability distribution and compute its marginal and conditional distributions | a, b, h, i, j, l | |||||||||||
5 | Calculate the probability, mean and variance of a RV that has either binomial, geometric or Poisson distribution, and apply the Poisson approximation to binomial distribution | a, b, h, i, j, l | |||||||||||
6 | Evaluate the probability of a normal RV, its mean and variance, and apply the normal approximation to binomial distribution | a, b, h, i, j, l | |||||||||||
7 | Distinguish the difference between population and sample, parameter and statistic | a, b, h, i, j, l | |||||||||||
8 | Apply the Central Limit Theorem (CLT) to the distribution of sample mean | a, b, h, i, j, l | |||||||||||
9 | Construct confidence interval for sample mean, and determine the sample size with appropriate margin of error | a, b, h, i, j, l | |||||||||||
10 | State the null and alternative hypotheses of a statistical test, determine the type I and type II errors, and compute its power and p-value | a, b, h, i, j, l | |||||||||||
11 | Apply a simple linear model to fit a dataset with 2 variables, calculate the values and construct confidence interval for the model coefficients, and perform prediction | a, b, h, i, j, l |
*Legend:
Fully consistent | (contributes to more than 75% of Student Learning Outcomes) | |
Partially consistent | (contributes to about 50% of Student Learning Outcomes) | |
Weakly consistent | (contributes to about 25% of Student Learning Outcomes) | |
[Blank] | Not related to Student Learning Outcomes |
The graduate attributes as stipulated by the EAB, are:
Lecture: Help you understand the motivation and definitions of the concepts and notions, approaches to solving problems in pursuant to learning outcomes
Tutorial: Develop problem solving skills, reinforce the understanding of the concepts and notions
Lectures (26 hours) | Help you understand the motivation and definitions of the concepts and notions, approaches to solving problems in pursuant to learning outcomes. LO: 1 to 11. |
Tutorials (12 hours) | Develop problem solving skills, reinforce the understanding of the concepts and notions. LO:1 to 11 |
Walpole, Myers, Myers, Ye, Probability and Statistics for Engineers and Scientists, 9th Edition, Pearson. ISBN-13:9780321629111
(1) General
Students are expected to complete all tutorial question, and take the quizzes. Students are expected to take responsibility to follow up with course notes, tutorials and course related announcements if they are absent.
(2) Absenteeism
Absence from quizzes and examination without a valid reason will affect your overall course grade. Valid reasons include falling sick supported by a medical certificate and participation in NTU’s approved activities supported by an excuse letter from the relevant bodies.
(3) Absence Due to Medical or Other Reasons
If you are sick and not able to attend the quizzes, you have to submit the original Medical Certificate (or another relevant document) to the administration to obtain official leave. In this case, the missed assessment component will not be counted towards the final grade. There are no make-up quizzes.
Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTU’s shared values.
As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.
Instructor | Office Location | Phone | |
---|---|---|---|
Yeo Kwee Poo (Asst Prof) | SPMS-MAS-04-16 | 6513-7456 | kweepoo@ntu.edu.sg |
Chan Song Heng (Assoc Prof) | SPMS-MAS-04-13 | 6513 7453 | chansh@ntu.edu.sg |
Week | Topic | Course ILO | Readings/ Activities |
---|---|---|---|
1 | Topic 1: Basic Probability Theory: • Sample space, Events, Counting Sample Points, Permutations & Combinations. • Probability, Equally Likely Outcomes, Not Equally Likely outcomes, Useful Rules • Conditional Probability, Independent Events, Partition, Bayes’ Rule | 1, 2 | Lecture notes |
2 | Topic 2: Random Variables & Probability Distribution: • Random Variables (RV), Discrete Random variables, Probability Mass Distribution, Cumulative Probability Distribution • Bernoulli Distribution and Binomial Distribution • Continuous Random variables, Probability Density Function, Cumulative Distribution Function | 3 | Lecture notes / Tutorial |
3 | Topic 3: Expectation & Variance : • Expectation of Discrete & Continuous RVs, Expectation of general RV, Useful Properties of Expectation, Variance & Properties | 3, 5 | Lecture notes / Tutorial |
4 | Topic 4: Joint Distribution : • Joint Probability Distribution & Marginal distribution (discrete RVs), Joint Probability Distribution & Marginal distribution (continuous RVs), Expectation E[g(X,Y)] • Conditional Probability Distribution, (Statistically) Independent RV. Variance, Covariance, Correlation coefficients, Useful Results | 4, 5 | Lecture notes / Tutorial |
5 | Topic 5: Special Discrete Probability Distributions : • Binomial, Geometric (return period), Poisson Distribution, Poisson Approximation | 5 | Lecture notes / Tutorial |
6 | Topic 6: Normal Distribution : • Normal Distribution, Standard Normal Distribution (introduction) • Standard Normal Distribution, Mean & Variance (Proofs excluded) • Applications: Problems, Approximation of Binomial Distribution | 6 | Lecture notes / Tutorial |
7 | Topic 7: Statistics: • Population & Parameters, Samples & Sample Statistics | 7 | Lecture notes / Tutorial |
8 | Topic 8: Sampling Distribution and Estimation : • Random Sampling, Sampling Distribution, Distribution of Sample Mean, Central Limit Theorem • Unbiased Estimator of variance, chi-sq-distribution, Samples with Unknown Population Variance, t-distribution • Sampling Distribution of Difference between two Means | 8, 9 | Lecture notes / Tutorial |
9 | Topic 9 Confidence Interval: • Confidence Intervals (introduction), Known/Unknown Variance, Large/Small Sample • Confidence Intervals (1-sided, 2-sided Confidence interval), Error, Size, Prediction Interval • 2-Population: confidence Interval, Small Size Unknown Variance | 9 | Lecture notes / Tutorial |
10 | Topic 9 Confidence Interval: • 2-Population: confidence Interval, Small Size Unknown Variance | 8, 9 | Lecture notes / Tutorial |
11 | Topic 10: Hypothesis Testing: • Introduction, Type-1, Type-2 Error • Hypothesis Testing for Population Mean (1-population), Power, p-value • Hypothesis Testing for Difference between Population Means | 10 | Lecture notes / Tutorial |
12 | Topic 11 Simple Linear Regression: • Linear Regression & Transformation • Estimation of Regression Parameters • Confidence Interval for Parameters in Linear Regression | 11 | Lecture notes / Tutorial |
13 | Revision | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 | Lecture notes |
Criteria | Standards | ||
Fail standard | Pass standard | High standard | |
Methods of approach | · Using methods that are irrelevant or do not apply to the given problem. · Invoking theorems whose conditions are not satisfied. | · Using relevant methods that help solve the problem. · Invoking theorems whose conditions are satisfied. | Finding methods and utilizing theorems that are both relevant and effective |
Validity of reasoning | Reasoning is logically invalid. | Reasoning is logically valid. | Reasoning is logically valid and effective. |
Clarity of argument | Reasoning is poorly explained or not explained at all. | Reasoning is clear but may contain some gaps. | Reasoning is clear, precise with no or insignificant gaps. |
Criteria | Standards | ||
Fail standard | Pass standard | High standard | |
Methods of approach | · Using methods that are irrelevant or do not apply to the given problem. · Invoking theorems whose conditions are not satisfied. | · Using relevant methods that help solve the problem. · Invoking theorems whose conditions are satisfied. | Finding methods and utilizing theorems that are both relevant and effective |
Validity of reasoning | Reasoning is logically invalid. | Reasoning is logically valid. | Reasoning is logically valid and effective. |
Clarity of argument | Reasoning is poorly explained or not explained at all. | Reasoning is clear but may contain some gaps. | Reasoning is clear, precise with no or insignificant gaps. |
Criteria | Standards | ||
Fail standard | Pass standard | High standard | |
Methods of approach | · Using methods that are irrelevant or do not apply to the given problem. · Invoking theorems whose conditions are not satisfied. | · Using relevant methods that help solve the problem. · Invoking theorems whose conditions are satisfied. | Finding methods and utilizing theorems that are both relevant and effective |
Validity of reasoning | Reasoning is logically invalid. | Reasoning is logically valid. | Reasoning is logically valid and effective. |
Clarity of argument | Reasoning is poorly explained or not explained at all. | Reasoning is clear but may contain some gaps. | Reasoning is clear, precise with no or insignificant gaps. |