Pokhara University
Faculty of Science and Technology
Course Information
- Course Code: MTH 216
- Course Title: Probability and Statistics (3-2-0)
- Nature of the Course: Theory
- Level: Bachelor
- Full Marks: 100
- Pass Mark: 45
- Total Lectures: 48 hours
- Program: BE
1. Course Description
This course is designed to familiarize students with various statistical methods and techniques for analyzing data. The contents include descriptive statistics, probability, probability distributions, sampling and estimation, hypothesis testing, simple correlation and regression analysis with emphasis on the engineering field.
2. General Objectives
- To familiarize students with various statistical methods and techniques for analyzing data.
- To impart analytical skills in the students required for the application of statistical methods for analyzing data in the field of engineering.
- To enable students with the skills to use real data in practical engineering-based applications.
3. Methods of Instruction
Lecture, Tutorial, Discussion, and Readings
4. Contents in Detail
Specific Objectives
- Identify concepts of statistics and its application in the field of engineering.
- Summarize, present, and compute various descriptive statistics.
Unit I: Introduction and Descriptive Statistics (4 hrs)
- Introduction of statistics and its applications in engineering
- Collection and presentation of data (Diagrammatic as well as graphical presentation)
- Measure of central tendency, location, and Measures of variability
Unit II: Probability (8 hrs)
- Basic probability, additive law, multiplicative law, and Bayes' theorem
- Random variables (Discrete and Continuous) and probability distribution function
- Mathematical expectation of random variables
Explain and apply discrete probability distributions (Binomial, Poisson distribution, Negative Binomial, and Hypergeometric distribution)
Unit III: Discrete Probability Distributions (4 hrs)
- Binomial distribution
- Poisson distribution
- Negative Binomial distribution
- Hypergeometric distribution
Unit IV: Continuous Probability Distributions (6 hrs)
- Rectangular or uniform distribution
- Normal distribution
- Gamma and Beta distributions
- Exponential distribution
Unit V: Bivariate Random Variables and Joint Probability Distribution (4 hrs)
- Joint probability mass function, Marginal probability mass function
- Joint probability density function, Marginal probability density function
Unit VI: Sampling Distribution and Estimation (7 hrs)
- Review of terms used in sampling
- Probability and non-probability sampling
- Sampling distribution of mean and standard error
- Central limit theorem
- Concept of point and interval estimation
- Sample size determination
- Confidence interval for single mean and difference of two population means and population proportion
Unit VII: Hypothesis Testing (8 hrs)
- Basic concept in hypothesis testing
- One sample test for mean and proportion
- Two sample test for mean and proportions
- Paired t – test
- ANOVA
- Chi-square test of independence
Unit VIII: Correlation and Regression (7 hrs)
- Simple correlation and its properties
- Simple linear regression
- Multiple regressions (Examples having only two independent variables)
Note: The figures in the parentheses indicate the approximate periods for the respective units.
5. List of Tutorials (30 Hours)
Numerical problems as demanded by the theory of each chapter will be assigned for the students and they are encouraged to solve the problems.
| Unit | Unit Name | List of Tutorials | Tutorial Hours |
|---|---|---|---|
| I | Introduction and Descriptive Statistics |
|
2 hrs. |
| II | Probability |
|
3 hrs. |
| III | Discrete Probability Distributions |
|
4 hrs. |
| IV | Continuous Probability Distributions |
|
5 hrs. |
| V | Bivariate Random Variables and Joint Probability Distribution |
|
3 hrs. |
| VI | Sampling Distribution and Estimation |
|
4 hrs. |
| VII | Hypothesis Testing |
|
5 hrs. |
| VIII | Correlation and Regression |
|
3 hrs. |
6. Evaluation System and Students’ Responsibilities
Evaluation System
In addition to the formal exam(s), the internal evaluation of a student may consist of quizzes, assignments, project work, class participation, etc. The tabular presentation of the internal evaluation is as follows:
| Internal Evaluation | Weight | Marks | External Evaluation Marks |
|---|---|---|---|
| Attendance & Class Participation | 10% | ||
| Assignments | 20% | ||
| Presentations/Quizzes | 10% | ||
| Term Exam | 60% | ||
| Total Internal | 50 | ||
| Semester-End Examination | 50 | ||
| Total Marks: 50 + 50 = 100 | |||
Student’s Responsibilities
Each student must secure at least 45% marks separately in internal assessment and practical evaluation with 80% attendance in the class in order to appear in the Semester End Examination. Failing to get such a score will be given NOT QUALIFIED (NQ) to appear in the Semester-End Examinations. Students are advised to attend all the classes, formal exams, tests, etc., and complete all the assignments within the specified time period. Students are required to complete all the requirements defined for the completion of the course.
7. Prescribed Books and References
Prescribed Books
- Johnson, R. A. (2018). Probability and Statistics for Engineers. New Delhi: Pearson Education Limited.
Reference Books
- Devore, J. L. (2010). Probability and Statistics for Engineering and Sciences. New Delhi: Cengage learning.
- Sheldom, M. R. (2014). Probability and Statistics for Engineers and Scientist. (4th edition), (8th edition), New Delhi: Cengage learning.
- Gupta, S.C & V.K. Kapoor. (2000). Fundamentals of Mathematical Statistics: A Modern Approach. (9th Revised edition) Sultan Chand & Sons Educational Publishers.