UCS 410-Probability and Statistics (Odd semester 2022-23)

Course Objectives: This course shall make the students familiar with the concepts of Probability and Statistics useful in implementing various computer science models. One will also be able to associate distributions with real-life variables and make decisions based on statistical methods.

Syllabus for the course UCS410:

Book to be followed: Probability & Statistics for Engineers & Scientists by R.E. Walpole et. al., Prentice Hall, (2016), 9th edition.

Lab Material:

Reference Books:

• Introduction to Probability and Statistics Using R by G. Jay Kerns

• Introductory_Statistics_with_R__2nd_ed

1. Experiment 1 pdf Sheet

2. Experiment 2 pdf Sheet

3. Experiment 3 pdf Sheet

4. Experiment 4 pdf Sheet

5. Experiment 5 pdf Sheet

6. Experiment 6 pdf Sheet

7. Experiment 7 pdf Sheet

8. Experiment 8 pdf Sheet

Practice sheets:

1. Practice Sheet 1_P&S

2. Practice Sheet 2_P&S

3. Practice Sheet 3_P&S

4. Practice Sheet 4_P&S

5. Practice Sheet 5_P&S

6. Practice Sheet 6_P&S

7. Practice Sheet-7_P&S

Lecture Notes:

• Lecture Slides_Unit-I_(Introduction to Statistics and Data Analysis):

1. Lecture 1-2_Introduction to Statistics and Data Analysis

2. Lecture 1-2 contd...Prerequisite (Mean, S.D. C.V.)

• Lecture Slides_Unit-II_(Probability):

3. (Lecture-3) Introduction to Probability (Sample Space, Events)

4. (Lecture-4) Axiomatic definition of Probability and addition rule with illustrations

5. (Lecture-5) Conditional Probability with illustrations

6. (Lecture-6) Independent Events with Examples

7. (Lecture-7) Total Probability theorem with illustrations

8. (Lecture-8) Bayes Theorem with illustrations

• Lecture Slides_(Unit –III & IV)_(Random Variables and their Special Distributions) :

9. (Lecture-9) Discrete and continuous random variables (Mean Variance)

10. (Lecture-10) Binomial Distribution with illustrations

11. (Lecture-10a) Uniform Discrete distribution

12. (Lecture-11) Geometric Distribution with Examples

13. (Lecture-12) Negative Binomial with Examples

14. (Lecture-13) Poisson distribution with illustrations

15. (Lecture-14) Concept of Hypergeometric Distribution with illustrations

16. (Lecture-15) Chebyshev’s and Markov’s inequality with illustrations

17. (Lecture-19) Transformation of function of random variable-Discrete and Continuous r.v.'s

18. (Lecture-20) Uniform or Rectangular distribution with illustrations

19. (Lecture-21) Exponential distribution with illustrations

20. (Lecture-22) Normal distribution with illustrations

21. (Lecture-23) Gamma distribution with illustrations

22. (Lecture-24) Chi-Square Distribution (Mean, Variance & M.g.f.)

23. (Lecture-25) Log-normal Distribution with illustrations

24. (Lecture-26) Transformation of two-dimensional random variables

• Lecture Slides_(Unit –V)_(Two Random Variables -Joint Distributions) :

25. (Lecture-16) Two dim r. v's-Joint probability distribution, Marginal and conditional distribution for DRV

26. (Lecture-17) Two-dim c.r.v's (joint, marginal and conditional dist. for CRV)

27. (Lecture-18) Two dim r.v. Conditional mean and variance, Correlation and regression, independence of random variables

• Lecture Slides_(Unit –VI & VII)_(Sampling Distributions and Theory of Estimation) :

28. (Lecture-27) (Sampling Distribution and The Central Limit Theorem

29. (Lecture-28) Chi-Square, t and F- Sampling distributions with illustrations

30. (Lecture-29) Theory of Estimation and consistency with illustrations

31. (Lecture-30) Maximum Likelihood Estimation with illustrations

32. (Lecture-31) Interval of Estimation and confidence interval with illustrations

Lecture Slides_(Unit – VIII)_(Testing of Hypothesis) :

33. (Lecture-32) Testing of Hypothesis-Large sample

34. (Lecture-33) Student's t-test- one sample mean

35. (Lecture-34) Chi square test of Goodness of fit

36. (Lecture-35) F-test for comparison of variances