Probability and Statistics

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