Probability and statistics syallabus

 

Pokhara University

Faculty of Science and Technology

Course Code: MTH 216

Course Title: Probability and Statistics (3-2-0)

Full Marks: 100

Pass Mark: 45

Nature of the Course: Theory

Total Lectures: 48 hours

Level: Bachelor

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 engineering field.

2. General Objectives

The general objectives of this course are:

• 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

Methods of instruction for this course include:

• Lecture
• Tutorial
• Discussion
• Readings

4. Contents in Detail

Unit I: Introduction and Descriptive Statistics (4 hrs)

• 1.1 Introduction of statistics and its applications in engineering
• 1.2 Collection and presentation of data (Diagrammatic as well as graphical presentation)
• 1.3 Measure of central tendency, location, and Measures of variability

Unit II: Probability (8 hrs)

• 2.1 Basic probability, additive law, multiplicative law, and Bayes' theorem
• 2.2 Random variables (Discrete and Continuous) and probability distribution function
• 2.3 Mathematical expectation of random variables

Unit III: Discrete Probability Distributions (4 hrs)

• 3.1 Binomial distribution
• 3.2 Poisson distribution
• 3.3 Negative Binomial distribution
• 3.4 Hyper geometric distribution

Unit IV: Continuous Probability Distributions (6 hrs)

• 4.1 Rectangular or uniform distribution
• 4.2 Normal distribution
• 4.3 Gamma and Beta distributions
• 4.4 Exponential distribution

Unit V: Bivariate Random Variables and Joint Probability Distribution (4 hrs)

• 5.1 Joint probability mass function, Marginal probability mass function
• 5.2 Joint probability density function, Marginal probability density function

Unit VI: Sampling Distribution and Estimation (7 hrs)

• 6.1 Review of terms used in sampling
• 6.2 Probability and non-probability sampling
• 6.3 Sampling distribution of mean and standard error
• 6.4 Central limit theorem
• 6.5 Concept of point and interval estimation
• 6.6 Sample size determination
• 6.7 Confidence interval for single mean and difference of two population means and population proportion

Unit VII: Hypothesis Testing (8 hrs)

• 7.1 Basic concept in hypothesis testing
• 7.2 One sample test for mean and proportion
• 7.3 Two sample test for mean and proportions
• 7.4 Paired t – test
• 7.5 ANOVA
• 7.6 Chi-square test of independence

Unit VIII: Correlation and Regression (7 hrs)

• 8.1 Simple correlation and its properties
• 8.2 Simple linear regression
• 8.3 Multiple regressions (Examples having only two independent variables)

List of Tutorials (30 Hours)

Unit I: Introduction and Descriptive Statistics

• 1.1 Collection and presentation of data (Diagrammatic as well as graphical presentation) - 1 hr.
• 1.2 Measure of central tendency, location, and Measures of variability - 1 hr.

Unit II: Probability

• 2.1 Basic probability, additive law, multiplicative law, and Bayes' theorem - 1 hr.
• 2.2 Random variables (Discrete and Continuous) and probability distribution function - 1 hr.
• 2.3 Mathematical expectation of random variables - 1 hr.

Unit III: Discrete Probability Distributions

• 3.5 Binomial distribution - 1 hr.
• 3.6 Poisson distribution - 1 hr.
• 3.7 Negative Binomial distribution - 1 hr.
• 3.8 Hypergeometric distribution - 1 hr.

Unit IV: Continuous Probability Distributions

• 4.1 Rectangular or uniform distribution - 1 hr.
• 4.2 Normal distribution - 2 hr.
• 4.3 Gamma and Beta distributions - 1 hr.
• 4.4 Exponential distribution - 1 hr.

Unit V: Bivariate Random Variables and Joint Probability Distribution

• 5.1 Joint probability mass function, Marginal probability mass function - 1 hr.
• 5.2 Joint probability density function, Marginal probability density function - 2 hr.

Unit VI: Sampling Distribution and Estimation

• 6.1 Sampling distribution of mean and standard error - 1 hr.
• 6.2 Central limit theorem - 1 hr.
• 6.3 Concept of point and interval estimation and Sample size determination - 1 hr.
• 6.4 Confidence interval for single mean and difference of two population means and population proportion - 1 hr.

Unit VII: Hypothesis Testing

• 7.1 One sample test for mean and proportion - 1 hr.
• 7.2 Two sample test for mean and proportions - 1 hr.
• 7.3 Paired t-test - 1 hr.
• 7.4 ANOVA - 1 hr.
• 7.5 Chi-square test of independence - 1 hr.

Unit VIII: Correlation and Regression

• 8.1 Simple correlation and its properties - 1 hr.
• 8.2 Simple linear regression - 1 hr.
• 8.3 Multiple regressions (Examples having only two independent variables) - 2 hr.

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
Attendance & Class Participation	10%	50
Assignments	20%
Presentations/Quizzes	10%
Term Exam	60%
Total Internal		Full 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

1. Johnson, R. A. (2018). Probability and Statistics for Engineers. New Delhi: Pearson Education Limited.

Reference Books

1. Devore, J. L.(2010). Probability and Statistics for Engineering and Sciences. New Delhi: Cengage learning.
2. Sheldon, M. R. (2014). Probability and Statistics for Engineers and Scientist. (4th edition), (8th edition), New Delhi: Cengage learning.
3. Gupta, S.C & V.K. Kapoor. (2000). Fundamentals of Mathematical Statistics: A Modern Approach. (9th Revised edition) Sultan Chand & Sons Educational Publishers.

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