Probability and Probability Distributions

By Dr. P.NAGESH | JSS Centre for Management Studies, Sri Jayachamarajendra College of Engineering MYSORE – 570 006

Learners enrolled: 813

About the course:
This course helps to understand the basic concepts concerned with probability, basic principles, permutations and combinations to probability, rules associated with probability, probability distribution in later chapters. concept of random variable, discrete and continuous random variables, expected value, variance and standard deviation of a random variable, expectation and variance of random variable in managerial decision making. Probability distribution, discrete and continuous probability distribution, discrete and continuous probability distribution, Binomial, Poisson and normal distributions, inferential statistics.

Summary

Course Status :	Completed
Course Type :	Elective
Duration :	12 weeks
Category :	Mathematics
Credit Points :	4
Level :	Undergraduate
Start Date :	09 Jan 2023
End Date :	30 Apr 2023
Enrollment Ends :	15 Mar 2023
Exam Date :

Page Visits

Course layout

Course Layout:
WEEK I

1. Definition of probability, classical and relative frequency approach to probability

2. Axiomatic Approach to Probability

3. Bayes theorem and its application

WEEK II

4. Expectation of a Random variable and its properties

5. Moment generating functions, their properties and uses

6. Discrete Uniform Distribution

WEEK III

7. Bernoulli Distribution

8. Binomial distribution

9. Poisson Distribution

WEEK IV

10. Geometric Distribution

11. Negative binomial distribution

12. Continuous Random Variable and Probability Density Function

WEEK V

13. Standard univariate continuous distributions and their properties

14. Uniform distribution

15. Gamma and Beta distributions

WEEK VI

16. Normal Distribution

17. Cauchy and logistic distributions

18. Pareto Distribution

WEEK VII

19. Bivariate Discrete & Continuous Distribution, its PMF & PDF

20. Bivariate moments and definition of raw and central product moments

21. Marginal and conditional distributions

WEEK VIII

22. Conditional Mean and Conditional Variance

23. Bivariate Normal Distribution (Part-I)

24. Bivariate Normal Distribution (Part-Il)

WEEK IX

25. Practical – Computing probability using addition and multiplication theorem

26. Conditional Probability and Independent Events

27. Practical – Computing probability using conditional probability and Baye’s theorem

WEEK X

28. Practical-Problems on PMF Variance, Expectation, Quartiles, Skewness and Kurtosis

29. Sketching the probability distribution functions

30. Practical-Computations of probabilities and fitting discrete distributions

WEEK XI

31. Sketching Distribution Functions and Density Functions

32. Computation of probabilities, expectation, moments & moment generating functions

33. Fitting Standard Univariate Continuous Distributions such as Normal and Exponential Distributions

WEEK XII

34. Simulation of Random Samples from Standard Univariate Continuous Distributions such as Normal, Exponential and Cauchy Distributions

35. Computing Marginal and Conditional Probability Distributions

36. Computing Marginal and Conditional Expectations

37. Drawing random samples from Bivariate Normal distribution

Books and references

Books and References:

1. Gupta, S.C, & Kapoor V.K, Fundamentals of Mathematical Statistics, Sultan Chand & sons.

2. Statistical Methods - N.G.Das, Tata McGraw-Hill Publishing Company Ltd, New Delhi.

3. Hogg R.V and Graig A.T (1978): Introduction to Mathematical statistics, Macmillan N.Y.

4. Mood, Graybill and Boes, Introduction to the Theory of Statistics McGraw-Hill.

5. V.K. Rohatgi; Probability Theory and Mathematical Statistics, Wiley Eastern Limited, New Delhi

6. Arun Kumar, Alka Chaudhry, Probability Theory, Krishna Prakashan Media (P) Ltd., Meerut (1st Edition-2004, 2nd Edition-2006, 4th Edition-2010).

7. G.C. Beri, Business Statistics, Tata McGraw Hill Education Private Limited (3rd Edition).

Instructor bio

Dr. P.NAGESH

JSS Centre for Management Studies, Sri Jayachamarajendra College of Engineering MYSORE – 570 006

Instructor Bio:
Subjects taught for MBA / PGDM / M.Tech. Programme

• Statistics for management

• Research Methods

• Quality Management / Engineering and many more under Management

Honors and Awards acknowledged

• Received 22 Innovative suggestion awards during the service at
M/s Kirloskar Electric Company Ltd., Belavadi Industrial Area, Mysore.

• Obtained 2 BEST PAPER awards for the session and conference with first place
at the National Conference PMGQ – 2005, Organized by Tyagarajar College of Engineering, Madurai, Tamil Nadu.

Publications:

• Published 22 International refereed Journals

• Published 25 National referred Journals

M.B.A. Thesis

Guided more than 300 students under VTU

M.Tech students

Guided 12 M.Tech students under VTU

Ph.D degree

FIVE candidates were awarded Ph.D degree from VTU , Belgaum.
Six candidates are pursuing Ph.D under VTU system.

Electronic lectures delivered.

Twice delivered EDUSAT programme:

Visvesvaraya technological University and ISRO developed joint Edusat programe.

Course certificate

Assessment/Assignment marks will be considered for Internal Marks and will carry 30 percent for overall Result.

End Term Exam- will have 100 questions and will carry 70 percent of overall Result.

*All students, who obtain 40% marks in in-course assessment and 40% marks in end-term proctored exam separately, will be eligible for certificate and credit transfer.

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