PROBABILITY AND STATISTICS (Optional Paper)

Paper Code: 
MAT325B
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
  1. Get knowledge about the foundations of probabilistic and statistical analysis. 
  2. Use probabilistic and statistical analysis in various applications in engineering and science.
  3. Get an idea about Random variable

Learning Outcomes

Learning and teaching strategies

Assessment

After the completion of the course the students will be able to:

CLO97- learn the concepts of random variables as outcomes of random experiments are introduced and the key properties of the commonly used standard univariate random variables are studied. Emphasis is placed on learning the theories by proving key properties of each distribution.

CLO98- students get a good understanding of exploratory data analysis.

CLO99- A good understanding of elementary probability theory and its application.

CLO100- students get ideas about the discrete and continuous distribution.

CLO101- students understand Some special mathematical expectations and study Marginal and conditional distributions, the correlation coefficient.

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical

 

 

 

Presentations by Individual Students

Class Tests at Periodic Intervals.

Written assignment(s)

Semester End Examination

 

Unit I: 
I
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: 
II
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: 
III
15.00

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

Unit IV: 
IV
15.00

Theoretical continuous distribution: 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: 
V
15.00

Correlation: 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, V.K.Kapoor, Fundamentals of Statistics, S.Chand & Sons, 2014.
  • J.N.Kapoor, H.C. Saxena, Mathematical Statistics, S.Chand & Co. Publications, 1960.
  • I.M.Chakravarthy, Handbook of Applied Statistics, Willey, 1967.
  • A.M.Mood, F.Graybill, Introduction to the Theory of Statistics, McGraw Hill, 1974.
References: 
  • B.Gnedenko, The Theory of Probability (MIR, Moscow), 6th Edition, 1988.
  • Pappu Kousalya, Probability, Statistics and Random Processes, Pearson, 2013.
  • Vijay K. Rohatagi, A.K.Md.Ehsanes Saleh, An Introduction to Probability and Statistics, Wiley, Second edition, 2008.
  • William Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Wiley,T hird edition, 2008.
  • A.M.Gun, M.K.Gupta, B.Dasgupta, Fundamentals of Statistics-Vol-II, World Press, 2016.
Academic Year: 
2019-2020
  • Printer-friendly version
  • PDF version