Introduction to Random Variables

Lecture Description

Introduction to random variables and probability distribution functions.

Course Description

Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!).

Course Index

1. Statistics: The Average
2. Sample vs. Population Mean
3. Variance of a Population
4. Sample Variance
5. Standard Deviation
6. Alternate Variance Formulas
7. Introduction to Random Variables
8. Probability Density Functions
9. Binomial Distribution 3
10. Expected Value: E(X)
11. Poisson Process 1
12. Poisson Process 2
13. Law of Large Numbers
14. Normal Distribution Excel Exercise
15. Introduction to the Normal Distribution
16. Qualitative Sense of Normal Distributions
17. Z-Score
18. Emperical Rule
19. Standard Normal Distribution and the Empirical Rule
20. More Emperical Rule and Z-Score Practice
21. Central Limit Theorem
22. Sampling Distribution of the Sample Mean Part 1
23. Sampling Distribution of the Sample Mean Part 2
24. Standard Error of the Mean
25. Sampling Distribution of the Sample Mean
26. Confidence Interval 1
27. Mean and Variance of Bernoulli Distribution Example
28. Bernoulli Distribution Mean and Variance Formulas
29. Margin of Error 1
30. Margin of Error 2
31. Confidence Interval Example
32. Small Sample Size Confidence Intervals
33. One-Tailed and Two-Tailed Tests
34. Z-statistics vs. T-statistics
35. Type 1 Errors
36. Small Sample Hypothesis Test
37. T-Statistic Confidence Interval
38. Large Sample Proportion Hypothesis Testing
39. Variance of Differences of Random Variables
40. Difference of Sample Means Distribution
41. Confidence Interval of Difference of Means
42. Clarification of Confidence Interval of Difference of Means
43. Hypothesis Test for Difference of Means
44. Comparing Population Part 1
45. Comparing Population Part 2
46. Hypothesis Test Comparing Population Proportions
47. Squared Error of Regression Line
48. Minimizing Squared Error to Regression Line Part 1
49. Minimizing Squared Error to Regression Line Part 3
50. Minimizing Squared Error to Regression Line Part 4
51. Regression Line Example
52. Minimizing Squared Error to Regression Line 2
53. R-Squared or Coefficient of Determination
54. Second Regression Example
55. Calculating R-Squared
56. Covariance and the Regression Line
57. Chi-Square Distribution Introduction
58. Pearson's Chi Square Test (Goodness of Fit)
59. Contingency Table Chi-Square Test
60. Calculating SST (Total Sum of Squares)
61. Calculating SSW and SSB (Total Sum of Squares Within and Between)
62. Hypothesis Test with F-Statistic