Engineering Mathematics-III (BTAM 302-23)

Course Objectives

This course aims to provide a solid foundation in probability and statistics, enabling students to:

• Understand fundamental concepts in probability and statistics
• Apply these concepts to analyze and interpret data
• Develop problem-solving skills in probability and statistics
• Use statistical software for data analysis

Course Outcomes

Upon completion of this course, students will be able to:

1. Apply concepts of probability to solve engineering problems
2. Analyze and interpret data using various statistical methods
3. Use statistical software for data analysis and visualization
4. Apply statistical inference techniques to draw conclusions from data
5. Design and conduct experiments, and analyze the results statistically

Detailed Syllabus

Part A

Unit-I: Probability & Random Variables

• Axioms of probability
• Conditional probability
• Bayes' theorem
• Random variables (discrete and continuous)
• Probability mass/density functions
• Cumulative distribution functions
• Mathematical expectation
• Moments
• Moment generating functions
• Characteristic functions

Unit-II: Probability Distributions

• Discrete Distributions:
  • Binomial
  • Poisson
  • Geometric
  • Negative binomial
  • Hypergeometric
• Continuous Distributions:
  • Uniform
  • Exponential
  • Normal
  • Gamma
  • Beta

Part B

Unit-III: Sampling Distribution & Statistical Inference

• Sampling distributions
• Central limit theorem
• Point estimation
• Interval estimation
• Hypothesis testing
• Tests for means and proportions
• Chi-square test
• t-test, F-test

Unit-IV: Correlation, Regression & Analysis of Variance

• Correlation and regression analysis
• Coefficient of determination
• Multiple regression
• Analysis of variance (ANOVA)
  • One-way
  • Two-way

Text/Reference Books:

• Miller, I. and Freund, J. E. (2006). Probability and Statistics for Engineers, 7th Ed., Prentice Hall of India.
• Ross, S. M. (2007). Introduction to Probability and Statistics for Engineers and Scientists, 4th Ed., Elsevier.
• Walpole, R. E., Myers, R. H., Myers, S. L., and Ye, K. (2012). Probability & Statistics for Engineers & Scientists, 9th Ed., Pearson.
• Montgomery, D. C., and Runger, G. C. (2014). Applied Statistics and Probability for Engineers, 6th Ed., Wiley.
• Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences, 8th Ed., Cengage Learning.