Introduction to Probability for Economics

Week 1

TOPIC
Descriptive Statistics (type of variables; frequency table; proportions and percentages; bar plot; histogram; mean, median and mode; outliers; range, variance and standard deviation; percentiles, quartiles and the box-plot; z-scores. The association between two categorical variables; contingency tables; conditional proportions).

EXPECTED LEARNING OUTCOMES
The student will be able to produce numerical and graphical summaries of data and interpret the results.

TEXTBOOK
§2.1 - §2.5
§3.1

EXERCISES
2.1 Practicing the Basics: 2.1 - 2.9
2.2 Practicing the Basics: 2.10-2.12, 2.21, 2.26
2.3 Practicing the Basics: 2.29 - 2.37, 2.39 - 2.45
2.4 Practicing the Basics: 2.46 - 2.47, 2.57
2.5 Practicing the Basics: 2.62, 2.64 - 2.71, 2.73 - 2.79
Chapter problems: 2.90 - 2.92, 2.103, 2.112, 2.119
3.1 Practicing the Basics: 3.1 - 3.3, 3.5 - 3.9

DATA
Titanic

IMAGES
Numerical and Graphical summaries

Week 2

TOPIC
Regression (the association between two quantitative variables; scatterplot; regression; correlation).
Probability (Random experiment, sample space and random event; axiomatic definition of probability; conditional probability; independence; Bayes theorem).

EXPECTED LEARNING OUTCOMES
The student will be able to use simple linear regression.
The student will be able to calculate the probabilities of random events and use Bayes’ rule.

TEXTBOOK
§3.2 - §3.3
§5.1 - §5.4

EXERCISES
3.2 Practicing the Basics: 3.11, 3.14-3.19
3.3 Practicing the Basics: 3.24 - 3.37
3.4 Practicing the Basics: 3.45 - 3.48
5.1 Practicing the Basics: 5.3, 5.6
5.2 Practicing the Basics: 5.13 - 5.23
5.3 Practicing the Basics: 5.28 - 5.31
5.4 Practicing the Basics: 5.47, 5.51, 5.56
Chapter problems: 5.71 - 5.77, 5.79 - 5.82, 5.86, 5.90, 5.100, 5.101, 5.105 - 5.116

DATA
Galton

IMAGES
2.6 Pearson Correlation Coefficients of 0
5.1 Scatter of Sons’ Heights v. Fathers’ Heights
From Spiegelhalter, D. (2019). The art of statistics: Learning from data. Penguin UK.

Week 3

TOPIC
Random Variables (Probability distribution of a discrete/continuous random variable; expectation and variance of a discrete/continuous random variables; Bernoulli distribution; binomial distribution; cumulative distribution function; normal distribution. quantile of the standardised normal random variable).

EXPECTED LEARNING OUTCOMES
The student will be able to use probability distributions for discrete and continuous random variables.

TEXTBOOK
§6.1 - §6.3

EXERCISES
6.1 Practicing the Basics: 6.1 - 6.15
6.3 Practicing the Basics: 6.35 - 6.46; 6.50 - 6.51
6.2 Practicing the Basics: 6.16 - 6.26
Chapter problems: 6.53, 6.64, 6.78, 6.80, 6.97

Week 4

TOPIC
Sample Mean and the Central Limit Theorem (Sampling proportion, sample mean, central limit theorem).

EXPECTED LEARNING OUTCOMES
The student will be able to approximate the distribution of the sample mean for large samples.

TEXTBOOK
§1.2
§7.2 - §7.1

EXERCISES
1.2 Practicing the Basics: 1.6 - 1.11, 1.13, 1.15
7.1 Practicing the Basics: 7.4, 7.8, 7.9, 7.11, 7.14
7.2 Practicing the Basics: 7.21, 7.24 - 7.26.

Week 5

TOPIC
Statistical Inference: Confidence Intervals and Hypothesis Testing (Point and interval estimation, margin of error, confidence interval for a mean/proportion; estimating the variance; null hypothesis; p-values; significance level and type I error) (Sampling proportion, sample mean, central limit theorem).

EXPECTED LEARNING OUTCOMES
The student will be able to calculate and interpret the confidence interval for a proportion and for the population mean.
The student will be able to test hypotheses about the population proportion and mean.

TEXTBOOK
§8.1 - §8.3
§9.1 - §9.4

EXERCISES
8.2 Practicing the Basics: 8.12 - 8.17, 8.19, 8.23
8.3 Practicing the Basics: 8.29, 8.30
9.3 Practicing the Basics: 9.28, 9.31, 9.38
9.4 Practicing the Basics: 9.43, 9.44, 9.48 - 9.52