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Probability and Statistics [1]

Paper Code: 
25MAT325(B)
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to –
  1. Explore about the foundations of probabilistic and statistical analysis. 
  2. Evaluate probabilistic and statistical analysis in various applications in engineering and science.
  3. Evaluate Random variable.
Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

25MAT

325(B)

 

 

 

 

 

Probability and Statistics

   (Theory)

 

 

 

 

CO125: Explore the concept of probability distributions, conditional probability and the applications of Bayes' theorem.

CO126: Identify different types of distribution functions. Explore the properties and characteristics of PMFs and PDFs.

CO127: Explore the concepts of binomial and Poisson distribution and their properties.

CO128: Evaluate and calculate the Normal distribution and curve fitting.

CO129: Explore methods of correlation and regression coefficients and their simple properties.

CO130: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions,  Topic  presentation, Assigned tasks

 

 

Quiz, Class Test, Individual projects,

Open Book Test, Continuous Assessment, Semester End Examination

 

 

 

Unit I: 
Theory of Probability and Random Variable:
15.00

Classical theory of probability, Laws of total and compound probability, Conditional probability, Baye’s theorem and related problems, Random variable, Discrete and continuous random variables. 

Unit II: 
Properties of random variables:
15.00

Distribution function, Probability mass function and probability density function, Bi-variate distributions, Conditional and Marginal distributions, Conditional expectation and variance, Co-variance, Analysis of bi-variate data.

Unit III: 
Discrete distributions:
15.00

Mathematical expectation and moment generating functions. Binomial and Poisson distributions with mean and variance, Poisson distribution as limiting case of binomial distribution.

Unit IV: 
Continuous distribution:
15.00

Normal distribution with its properties related problems, Fitting of curves: Principle of curve fitting, Fitting of straight line and second degree parabola by least squares method.

Unit V: 
Correlation and regression:
15.00

Definition and types, Properties of correlation, Methods of studying correlation: Karl Pearson’s coefficient of correlation, Spearman Rank Correlation, Linear Regression: Definition, Fitting of two lines of regression, Regression coefficients with simple properties.

Essential Readings: 
  • S.C. Gupta and V.K. Kapoor, Fundamentals of Statistics, S.Chand & Sons, 2014.
  • J.N. Kapoor and H.C. Saxena, Mathematical Statistics, S.Chand & Co. Publications, 2010.
  • I. M. Chakravarthy, Handbook of Applied Statistics, Willey, 1967.
  • A. M. Mood and F. Graybill, Introduction to the Theory of Statistics, McGraw Hill, 2017.
  • B. Gnedenko, The Theory of Probability (MIR, Moscow), 6th Edition, 1998.
References: 
  • A.M. Gun, M.K. Gupta and B. Dasgupta, Fundamentals of Statistics-Vol-II, World Press, 2016. 
  • Pappu Kousalya, Probability, Statistics and Random Processes, Pearson, 2013.
  • William Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Wiley, Third edition, 2008.
  • Vijay K. Rohatagi, A. K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics, Wiley, Second edition, 2008.
 
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Academic Year: 
2025-2026 [10]

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