Concepts and Notions for EconometricsProbability and Statistics

Table of contentsProbability: 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 Shape Mean vs. Median

Symmetric Mean nearly equal to median

Skewed left Mean smaller than the median

Skewed right Mean 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