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 undergraduateINDUSTRY 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.
Week 1: 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