About the course:
The use of statistical reasoning and methodology is indispensable in modern world. It is applicable to every discipline, be it physical sciences, engineering and technology, economics or social sciences. Much of the advanced research in electronics, electrical, computer science, industrial engineering, biology, genetics, and information science relies increasingly on use of statistical tools. It is essential for the students to get acquainted with the subject of probability and statistics at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application oriented problems.

INTENDED AUDIENCE : Any Interested Learners.

PREREQUISITES : Must have good knowledge of Differential and Integral Calculus, sequences and series, Basic Linear/Matrix Algebra (usually students who have completed Mathematics-I and II at first year undergraduate

PREREQUISITES : Must have good knowledge of Differential and Integral Calculus, sequences and series, Basic Linear/Matrix Algebra (usually students who have completed Mathematics-I and II at first year undergraduate

INDUSTRY SUPPORT : Today all industries use statistical methods. So for students desirous to work in any type of industry, this course will be indispensable. In particular, companies dealing with Business Analytics, Banking and finance, Insurance machine learning, data mining etc. this course will be invaluable.

1. Sets, Classes, Collections

2. Sequence of Sets

3. Ring, Field (Algebra)

4. Sigma-Ring, Sigma-Field, Monotone Class

5. Random Experiment, Events

6. Definitions of Probability

7. Properties of Probability Function-I

8. Properties of Probability Function-II

Week 2:

9. Conditional Probability

10. Independence of Events

11. Problems in Probability-I

12. Problems in Probability-II

13. Random Variables

14. Probability Distribution of a Random Variable-I

Week 3:

15. Probability Distribution of a Random Variable-II

16. Moments

17. Characteristics of Distributions-I

18. Characteristics of Distributions-II

19. Special Discrete Distributions-I

20. Special Discrete Distributions-II\

Week 4:

21. Special Discrete Distributions-III

22. Poisson Process-I

23. Poisson Process-II

24. Special Continuous Distributions-I

25. Special Continuous Distributions-II

26. Special Continuous Distributions-III

Week 5:

27. Special Continuous Distributions-IV

28. Special Continuous Distributions-V

29. Normal Distribution

30. Problems on Normal Distribution

31. Problems on Special Distributions-I

32. Problems on Special Distributions-II

Week 6:

33. Function of a Random Variable-I

34. Function of a Random Variable-II

35. Joint Distributions-I

36. Joint Distributions-II

37. Independence, Product Moments

38. Linearity Property of Correlation and Examples

Week 7:

39. Bivariate Normal Distribution-I

40. Bivariate Normal Distribution-II

41. Additive Properties of Distributions-I

42. Additive Properties of Distributions-II

43. Transformation of Random Variables

44. Distribution of Order Statistics

Week 8:

45. Basic Concepts

46. Chi-Square Distribution

47. Chi-Square Distribution (Cont…), t-Distribution

48. F-Distribution

49. Descriptive Statistics – I 50. Descriptive Statistics – II

Week 9:

51. Descriptive Statistics – III

52. Descriptive Statistics – IV

53. Introduction to Estimation

54. Unbiased and Consistent Estimators

55. LSE, MME 56. Examples on MME, MLE

Week 10:

57. Examples on MLE-I

58. Examples on MLE-II, MSE

59. UMVUE, Sufficiency, Completeness

60. Rao-Blackwell Theorem and its Applications

61. Confidence Intervals-I

62. Confidence Intervals- II 63. Confidence Intervals- III\

Week 11:

64. Confidence Intervals- IV

65. Basic Definitions

66. Two Types of Errors

67. Neyman-Pearson Fundamental Lemma 68. Applications of N-P Lemma-I

69. Applications of N-P Lemma-II

Week 12:

70. Testing for Normal Mean

71. Testing for Normal Variance

72. Large Sample Test for Variance and Two Sample Problem

73. Paired t-Test

74. Examples

75. Testing Equality of Proportions

1. An Introduction to Probability and Statistics by V.K. Rohatgi & A.K. Md. E. Saleh

2. Probability and Statistical Inference by Hogg, R. V., Tanis, E. A. & Zimmerman D. L.

3. Probability and Statistics in Engineering by W.W. Hines, D.C. Montgomery, D.M. Goldsman, C.M. Borror

4. Introduction to Probability and Statistics for Engineers and Scientists by S.M. Ross

5. Introduction to Probability and Statistics by J.S. Milton & J.C. Arnold.

6. Introduction to Probability Theory and Statistical Inference by H.J. Larson

7. Probability and Statistics for Engineers and Scientists by R.E. Walpole, R.H. Myers, S.L. Myers, Keying Ye

8. Modern Mathematical Statistics by E.J. Dudewicz & S.N. Mishra

9. Introduction to the Theory of Statistics by A.M. Mood, F.A. Graybill and D.C. Boes

2. Probability and Statistical Inference by Hogg, R. V., Tanis, E. A. & Zimmerman D. L.

3. Probability and Statistics in Engineering by W.W. Hines, D.C. Montgomery, D.M. Goldsman, C.M. Borror

4. Introduction to Probability and Statistics for Engineers and Scientists by S.M. Ross

5. Introduction to Probability and Statistics by J.S. Milton & J.C. Arnold.

6. Introduction to Probability Theory and Statistical Inference by H.J. Larson

7. Probability and Statistics for Engineers and Scientists by R.E. Walpole, R.H. Myers, S.L. Myers, Keying Ye

8. Modern Mathematical Statistics by E.J. Dudewicz & S.N. Mishra

9. Introduction to the Theory of Statistics by A.M. Mood, F.A. Graybill and D.C. Boes

Prof. Somesh Kumar is a professor in the Department of Mathematics, IIT Kharagpur. He has over 32 years of experience of teaching courses on Probability Statistics, Statistical Inference, Sampling Theory, Stochastic Processes, Multivariate Analysis, Regression Analysis, Time Series, Experimental Designs, Decision Theory to undergraduate, postgraduate and doctorate students. His NPTEL courses (under MHRD) on Probability and Statistics, Statistical Inference and Statistical Methods for Scientists and Engineers (each of 40 hours) are available online and very popular. He has also taught Mathematics-I in QEEE program of MHRD to 130 engineering college students in online mode during Autumn 2014-2015. He offered the course “Probability and Statistics” for certification program in Jan-April 2016, Jan-April 2017, Jan-April 2019. He also offered the course “Statistical Inference” for certification program during Jan-April 2019. His lectures on “Probability” and “Permutation and combinations” for class XII students under IIT-PAL scheme of MHRD are also available through DTH channels of national television.

His research interests are Statistical Decision Theory, Estimation Theory, Testing of Hypothesis, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 100 research papers in refereed reputed international journals and book chapters. He has supervised eleven Ph.D. students and more than two hundred fifty Masters (M.Tech./ M.Sc./B.Tech.) dissertations.

He has been guest professor in University of Ulm, Germany in July 2017 and June-July 2018 and in University of Dortmund in May-June 2019. He is Principal Investigator for a major research project “Drone for Vaccine Delivery” funded by the Indian Council for Medical Research. He has delivered invited lectures in various universities in India and abroad.

His research interests are Statistical Decision Theory, Estimation Theory, Testing of Hypothesis, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 100 research papers in refereed reputed international journals and book chapters. He has supervised eleven Ph.D. students and more than two hundred fifty Masters (M.Tech./ M.Sc./B.Tech.) dissertations.

He has been guest professor in University of Ulm, Germany in July 2017 and June-July 2018 and in University of Dortmund in May-June 2019. He is Principal Investigator for a major research project “Drone for Vaccine Delivery” funded by the Indian Council for Medical Research. He has delivered invited lectures in various universities in India and abroad.

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:**30 April 2023** Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

**CRITERIA TO GET A CERTIFICATE**

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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