Concepts and Notions for Econometrics Probability and Statistics

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

Definition of probability

Conditional probability

Independance of events

Random variables

The Normal Probability Distribution

Properties of the Normal Distribution

The standard Normal Distribution

Point estimate

Sampling distribution

Central Limit Theorem for sample proportions

Central Limit Theorem for sample means

The properties of Central Limit Theorem

Hypothesis testing

Possible Outcomes for a Hypothesis Test

Summary of Hypothesis Tests

Measures of Central Tendancy

Mean or average By definition of mean

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

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

Variance and standard deviation

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?

Covariance

Correlation (I)

Correlation (II)

Properties of correlation coefficients

Correlation and causation

The Z-score or standard score