1. Concepts and Notions for Econometrics Probability and Statistics

2. Table of contents Probability: Slide 3 Independence of events: Slide 5 Random variables: Slide 6 Normal Probability: Slide 9 Central Limit Theorem: Slide 21 Hypothesis testing: Slide 27 Mean, median : Slide 36 Variance and standart deviation : Slide 44 Covariance : Slide 47 Z-score : Slide 53

3. Definition of probability

4. Conditional probability

5. Independance of events

6. Random variables

9. The Normal Probability Distribution

10. Properties of the Normal Distribution

17. The standard Normal Distribution

19. Point estimate

20. Sampling distribution

21. Central Limit Theorem for sample proportions

22. Central Limit Theorem for sample means

23. The properties of Central Limit Theorem

27. Hypothesis testing

29. Possible Outcomes for a Hypothesis Test

34. Summary of Hypothesis Tests

36. Measures of Central Tendancy

37. Mean or average By definition of mean

39. The most appropriate measure of central tendency will depend on the data. The mode can be used for both qualitative and quantitative data. For small data sets (relatively few observations) the mean is influenced by extreme values, but the median is resistant. For large data sets (many observations) the mean and median tend to be close to each other. The mean is easier to calculate than the median since we do not have to sort the data. Pros and Cons of the Mean, Median, and Mode

40. Identifying the Shape of a Distribution Distribution ShapeMean vs. Median SymmetricMean nearly equal to median Skewed leftMean smaller than the median Skewed rightMean larger than the median

44. Variance and standard deviation

47. Covariance and Correlation Questions: What does it mean to say that two variables are associated with one another? How can we mathematically formalize the concept of association?

48. Covariance

49. Correlation (I)

50. Correlation (II)

51. Properties of correlation coefficients

52. Correlation and causation

53. The Z-score or standard score