Probability and Probability Distributions

By Dr. P.NAGESH   |   JSS Centre for Management Studies, Sri Jayachamarajendra College of Engineering MYSORE – 570 006
Learners enrolled: 1017
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 Start Date : 17 Jan 2022 End Date : 11 Apr 2022 Exam Date : Enrollment Ends : 28 Feb 2022 Category : Mathematics Credit Points : 4 Level : Undergraduate

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).

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.