-Probability and Statistical Distributions-ECON-221 & ECON-222-Statistical Estimation and Inference-

Lecture notes: (PDF) (Page) Section information and grades: (221 (GSHEET)) (222 (GSHEET))

Whiteboards: 221: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) | 222: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

When you request access to Whiteboards from a Zoom account which is not licensed by Bilkent University, the system does not allow me to share. You should access your Zoom credentials via SRS and then try to view the Whiteboards: After logging into your STARS account, click/visit "Request Zoom License" and submit your demand. You'll receive an email that will enable you to enter your Zoom account licensed by Bilkent University. Once this is done, you'll be able to view the Whiteboards without additional authorization. Thanks are due to Güneş Hergül for providing the instructions.

‘Would you tell me, please, which way I ought to go from here?’ | ‘That depends a good deal on where you want to get to,’ said the Cat. | ‘I don't much care where--‘ said Alice. | ‘Then it doesn't matter which way you go,' said the Cat. | ‘--so long as I get SOMEWHERE,' Alice added as an explanation. | ‘Oh, you're sure to do that,’ said the Cat, ‘if you only walk long enough.’ | [Alice’s Adventures in Wonderland, Lewis Carroll]

Question: What is effective learning?

Answer: Effectiveness is the degree to which a process delivers a 'desired outcome', which is to me to see my students as high-caliber members of the professional and academic community, even more rewardingly to see my former students as people bringing positive change to the society.

Question: What is effective learning from the perspective of a student?

Answer: That depends a good deal on where you want to get to. See the previous Q/A to form your personal answer.

Question: Should I attend each class hour?

Answer: There is a strong association between performance and attendance.

Question: So, showing up in class is enough, right?

Answer: “To attend” does not only mean “to show up”, it rather has a connotation with “to come to class prepared and to participate”.

Question: Is classroom a boring environment?

Answer: No, as longs as everyone behaves with basic politeness and civility. An informal atmosphere is acceptable as long as it is orderly.

Question: I have a good memory; can I rely on it?

Answer: Memorization has some role in triggering your learning, but it should eventually be replaced with a full command of the subject matter. I usually refer to a revised version of Benjamin Bloom's work (Bloom's Taxonomy of Educational Objective) with the addition of the psycho-motor domain (as developed by Harrow, 1972) to view the cognitive domain: "

Knowledge: recognizing or recalling information (~memorization)
Comprehension: organizing and arranging material mentally; grasp a topic; collect together a battery of information and ideas
Application: applying the previously learned to reach an answer
Analysis: thinking critically and in depth; solving problems
Synthesis: thinking creatively to present something original; producing original communications, making predictions and solving problems
Evaluation: judging the value or validity of an idea, a solution to a problem, or an aesthetic work; offering an opinion on an issue through objective criteria, standards or personal values "

Based on this, every course has a pre-designed target complexity over the Knowledge-to-Evaluation spectrum. ECON 221 reaches mostly upto Application and partly Analysis, while ECON 222 reaches upto Synthesis and Evaluation.

Question: How long should I study?

Answer: See the previous Q/A.

Question: What gear do I need?

Answer: Each student is suggested to have a 'traditional notebook + pencil' or 'tablet with notetaking capacity' and a calculator for exams.

Question: I will never cheat. But what happens to cheaters?

Answer: Cheating ~ plagiarism is unfair and may be penalized at a minimum with failing the course and at a maximum with suspension.

Question: Is there an AI policy?

Answer: ECON 221 and ECON 222 do not employ AI in teaching. However, students may assist themselves with AI while they are studying the subject matter. See also the previous Q/A.

Question: What are the exam rules? How can I learn about the exam logistics?

Answer: See the very end of this page.

Question: When is Office Hours?

Answer: Office hours are the time slots dedicated to answer the students' course-related questions and other queries; students may come to A-108 without appointment, except for the first week of classes & the final exams period. Office hours in Fall 2025 are to be held every Wednesday from 11:00 to 13:00.

Question: OK. I'm ready to go for it. Where can I find the Lecture Notes from?

Answer: PDF version of Lecture Notes is available at Lecture notes (PDF) and HTML version is at Lecture notes (Page).

Question: Can I also reach the previous semesters' materials?

Answer: Yes, indeed. These are available at Past materials (Folder).

Also,

Statistical distributions practice file (221 and 222) is at SD (XLSX),

Confidence intervals practice file (222) is at CI (XLSX),

Hypothesis testing practice file (222) is at HT (XLSX),

Selected distribution tables are at z (PDF, PNG) t (PDF, PNG) Chi2 (PDF, PNG) F (PDF),

and, Microsoft Excel function reference is at Excel (Page).

You don't need to return to this point every time, these links are repeatedly given below when needed.

Question: How are the official announcements made?

Answer: Via emails sent by the teacher through STARS/AIRS/SRS platform. So, make sure your email address registered with the University receives these emails.

Question: What are the topics to be covered? How should I proceed now?

Answer: Simply bookmark this page in your favorite browser & use it & come to classes regularly.

https://stars.bilkent.edu.tr/syllabus/view/ECON/221

Excel (Page)

1 Describing data

1.1 A taxonomy of data types

1.2 What is a "data set"?

1.3 Frequency

010 Microsoft Excel basics - preparing tables and entering formulas.xlsx ECON 221 Rec 1

020 Preparing histograms using COUNTIF to describe data.xlsx ECON 221 Rec 1

1.4 Representation of distributions

1.5 Measures of central tendency

1.6 Measures of dispersion

Self study Income distribution in Türkiye

221 Handout 240214 - Mean - Variance - Covariance.pdf ECON 221 Rec 2 [Brief review of handout]

030 Use of PERCENTILEs to describe data.xlsx ECON 221 Rec 2

1.7 Measures of association for bivariate data

1.8 Issues of unit and scale

1.9 Chebyshev’s theorem (Chebyshev’s inequality)

1.10 Adding and multiplying terms over an index

040 Generating random numbers - Linear Cogruential Generator - Using the digits of Pi.xlsx ECON 221 Rec 3

050 Describing data via histograms to reveal Global warming using COUNTIFS.xlsx ECON 221 Rec 4

060 Preparing Cross Tabulations using PIVOT TABLE and calculating Conditional probabilities.xlsx

070 Describing data via PIVOT TABLEs to reveal Global warming.xlsx

221 Hw1 due 20 October 2025 Monday 13:30 Go to Income distribution in Türkiye which was referenced above as Self study before. Examine the page including all its links and data tables. Your task is to prepare a report on 'how fair the income distribution in Türkiye is', i.e., whether it is fair; if not, what makes you to conclude it isn't. In that, first learn on your own the terms 'fair', 'just', 'equal' and 'equitable' referring to economics textbooks and/or AI of your choice. Your quantitative assessment must be based on what you've learned in Chapter 1, where your knowledge therein should enable you to learn new things you'll encounter, so, do your research. Once your analysis is done, prepare a research note (a short paper) of 1500 to 2000 words that includes all of the following: 'Title', 'Abstract (100-120 words)', 'Keywords', 'Introduction', 'Literature Review', 'Methodology (refer to Lecture Notes)', 'Empirical Analysis', 'Discussion and Conclusion', 'References (a max of 5)'. Your paper will not have an Appendix or Appendices, the number of footnotes can be a maximum of 5 and endnotes are not allowed. Use of AI in writing is not suggested; write your work on your own. Regarding the format of your paper (format elements: fonts, spacing; captions: enumeration and titling of visuals; layout elements: page structure and enumeration, etc.), briefly review the published empirical papers of the faculty members of your department and maintain the format of one of those published after 2020. If you are not from ECON or MAN, refer to ECON faculty's papers. Cite this guiding paper in your References. Print your report to file in PDF format. Finalize your Excel file (just one) used in analysis so that it will be self-explanatory and it will include everthing done. Your files must be named as: 221-Hw1-11111111.pdf and 221-Hw1-11111111.xlsx, where 11111111 is your ID number. Not naming your files as described will result in the rejection of your submission. Submit both files in the same email message as 'file attachments' (not 'cloud-based links') to your TA's email address with proper salutation and body text. Upon receiving your submission, your TA will send you a message including the word "Received". Grading: No submission=0 points, Late submission=15 points deduction. Other deductions will be announced by the TA team. Note that Homework performance makes up 20%of your semester total; so, sharing your work in any form with other students may harm your individual letter grade assessment. Unacceptably high similarity between submissions will yield a grade of 0 points as well as possible disciplinary investigation. Unless otherwise noted, these rules apply to all Homework assignments.

Excel (Page)

2 Probability basics

2.1 Modeling a Random Experiment

2.2 Properties of a probability measure: Probability postulates

2.3 Probability versus possibility

2.4 Methods of assigning probability

2.5 Counting

221 Handout 240219 - Exercises on Probability basics.pdf

2.6 Conditional probability

2.7 Bayes’ Theorem

2.8 Independence of events

2.9 Bivariate probabilities

2.10 Joint, marginal and conditional probabilities

2.11 Independence of Events ECON 221 is here [221 Mt1 up to here: except for Bayes' Theorem]

221 Handout 240305 - Conditional probability - Independence of events.pdf

221 Hw2 due DD MMM YYYY Day HH:MM Hw description

221 Hw3 due DD MMM YYYY Day HH:MM Hw description

SD (XLSX) z (PDF, PNG) Excel (Page)

3 Random variables

3.1 Random Variables

3.2 Cumulative distribution function: CDF

3.3 Continuous and discrete random variables

3.4 Probability distribution functions

3.5 Expected Value

221 Handout 240426 - Exercises on PDF - CDF - Expected value.pdf

3.6 Variance and standard deviation

3.7 Random variables and distributions: Discrete probability laws

3.8 Random variables and distributions: Continuous probability laws

221 Handout 241217 - Approximations to Binomial - CT - LOLN - CLT.pdf

080 Generating random numbers using RAND and the Inverse Transformation Technique - 1.xlsx ECON 222 Rec 1

090 Generating random numbers using RAND and the Inverse Transformation Technique - 2.xlsx ECON 222 Rec 1

100 Solving a Bayes theorem question via Simulation.xlsx

110 Conditional probabilities Statistical Independence - an exercise on student performance.xlsx

120 Simulating the Geometric distribution.xlsx

130 Simulating the Negative Binomial distribution.xlsx

140 Simulating Poisson arrivals of customers via Exponential interarrival times - Inverse Transformation Technique.xlsx

150 Inverse Transformation Technique and calculating Expected Value via simulation for an interesting distribution.xlsx

160 Inverse Transformation Technique and calculating Expected Value via simulation for the Logistic distribution.xlsx

170 Inverse Transformation Technique for a semicircularly shaped distribution .xlsx

180 Simulating a Galton Board.xlsx ECON 222 Rec 2

190 Simulating an asymmetric Galton Board.xlsx

200 Calculating Expected Value via simulation - Miner question.xlsx

210 Calculating Expected Value via simulation - an advanced exercise.xlsx

220 Estimating pandemic-epidemic probabilities for the future - an advanced exercise.xlsx

230 Poisson arrivals via Exponential interarrival times and the Law of Large Numbers theorem.xlsx ECON 222 Rec 2

221 Hw4 due DD MMM YYYY Day HH:MM Hw description

3.9 Random variables and distributions: Moments of distributions [Optional material]

3.10 Moment generating functions [Optional material]

3.11 Random vectors [Optional material]

SD (XLSX) z (PDF, PNG) Excel (Page)

4 Sampling distributions

4.1 Chebyshev’s theorem

4.2 Law of large numbers theorem

4.3 Central limit theorem

4.4 Distribution of sample means

240 Sampling from a finite population using RAND-INDEX-RANK combination.xlsx ECON 222 Rec 3

222 Hw1 due 20 October 2025 Monday 13:30 Create two towns: town A with 5000 and town B with 1000 residents (citizen, person living in town). Each town will be on a separate worksheet of the same Excel workbook. Each citizen will be represented in a row with the following attributes: incomes in town A will come from an Exponential (1/100000) and incomes in town B will come from a Normal(100000, 225000000) distribution. Each citizen in each town will support either political party X or political party Y: in town A, each citizen has an independent probability of 0.60 to vote for X; in town B, it is 0.40. In each town half of the population is women and half is men. In this Homework, there is no statistical dependence between income, political tendency and gender variables; you'll introduce these in a subsequent homework. Note that, lambda, mu, sigma-square and P (figure out which is which) must be parameters in Excel, i.e., when you change them in their designated cells, incomes, political tendencies and genders must change. While submitting your work, the given parameters must be effective on your file. Make sure you've generated the distributional graphs and a rich set of descriptive statistics: go to Chapter 1. For each distributional parameter, check and document if the experimentally obtained (empirical) parameters match the theoretical (input) ones. Use of AI is not suggested in this homework. Once your work is done, annotate your Excel file with text boxes & make all necessary explanations therein: what you did, how you did & why you did must all be crystal-clear. Your file (just one) must be named as: 222-Hw1-11111111.xlsx, where 11111111 is your ID number. Not naming your file as described will result in the rejection of your submission. Submit the file in an email message as a 'file attachment' (not a 'cloud-based link') to your TA's email address with proper salutation and body text. Upon receiving your submission, your TA will send you a message including the word "Received". Grading: No submission=0 points, Late submission=15 points deduction. Other deductions will be announced by the TA team. Note that Homework performance makes up 20%of your semester total; so, sharing your work in any form with other students may harm your individual letter grade assessment. Unacceptably high similarity between submissions will yield a grade of 0 points as well as possible disciplinary investigation. Unless otherwise noted, these rules apply to all Homework assignments.

221 Hw5 due DD MMM YYYY Day HH:MM Hw description

https://stars.bilkent.edu.tr/syllabus/view/ECON/222

SD (XLSX) z (PDF, PNG) Excel (Page)

[Chapter 5 will be skipped for a while. When its time comes, you'll be notified here.]

5 Point estimators

5.1 Point estimation

5.2 Least squares technique: LS

5.3 Maximum likelihood technique: ML

5.4 Method of moments technique: MM

250 Sampling via RAND-INDEX-RANK in the German tank problem.xlsx ECON 222 Rec 4 [Go over the German tank problem first]

SD (XLSX) CI (XLSX) z (PDF, PNG) t (PDF, PNG) Chi2 (PDF, PNG) Excel (Page)

6 Confidence intervals

6.1 Confidence interval estimation: One population

6.2 Finite populations and correction

6.3 Sample size determination ECON 222 is here [222 Mt1 up to here]

6.4 Confidence interval estimation: Two populations

222 Handout 240221 - Confidence interval estimation 1.pdf

222 Handout 240226 - Confidence interval estimation 2.pdf

260 Simulating the voting behavior in a small town to understand Population Proportion.xlsx

280 Confidence intervals to reveal Global warming.xlsx

290 Confidence interval estimation for Population Proportion in a small town - sampling via RAND-INDEX-RANK.xlsx

300 Confidence interval estimation for Population Proportion - individual town and countrywide results.xlsx

310 Confidence interval estimation for Population Proportion in a small town - Finite Population Correction.xlsx

320 Assessing the forecast performance via Confidence intervals.xlsx

330 Limit of Chi-square(m) by m is 1 as m tends to infinity - via simulation.xlsx

222 Hw2 due DD MMM YYYY Day HH:MM Hw description

222 Hw3 due DD MMM YYYY Day HH:MM Hw description

SD (XLSX) CI (XLSX) HT (XLSX) z (PDF, PNG) t (PDF, PNG) Chi2 (PDF, PNG) F (PDF) Excel (Page)

7 Hypothesis testing

7.1 Hypothesis testing: One population

222 Handout 240311 - Hypothesis testing.pdf

7.2 Hypothesis testing: Two populations

222 Handout 240312 - Two population procedures.pdf

7.3 p-value

7.4 Type I and Type II errors and the Power of a hypothesis test

222 Handout 240325 - p-value and Power.pdf

340 Assessing the forecast performance via Hypothesis testing.xlsx

350 Disclosure of ballot box results after an election - Confidence intervals and Hypothesis testing.xlsx

360 ANOVA - Analysis of Variance.xlsx

222 Hw4 due DD MMM YYYY Day HH:MM Hw description

SD (XLSX) CI (XLSX) HT (XLSX) z (PDF, PNG) t (PDF, PNG) Chi2 (PDF, PNG) F (PDF) Excel (Page)

8 Linear regression analysis

8.1 Overview of linear models

8.2 Transformations and functional forms

8.3 Our approach to teaching/learning

8.4 Building and estimating an Unconditional Model of Mean: A model which is a non-model

8.5 Building and estimating a Simple Linear Regression model

8.6 Building and estimating a Multiple Linear Regression model: An increase in dimensionality

8.7 Goodness of fit

8.8 Handling statistical uncertainty: calculation of variances and covariances associated with a Multiple Linear Regression model

8.9 Statistical inference

222 Handout 241213 - For inference exercises.pdf

8.10 Essence of the Gauss-Markov assumptions

222 Handout 241217 - MLR model summary.pdf

8.11 Model Specification

SD (XLSX) CI (XLSX) HT (XLSX) z (PDF, PNG) t (PDF, PNG) Chi2 (PDF, PNG) F (PDF) Excel (Page)

Some dedicated Statistical/Econometric software and other software platforms that support Statistical/Econometric computations are:

EViews Stata R & RStudio Python Matlab JASP Minitab SPSS

Descriptions

8.12 Regression analysis at work

222 Handout 240506 - Regression analysis at work.pdf

case00.wf1 case00.xlsx

Case 01 State public expenditures in the US: A public finance model (Economics)

Data reference: U.S. Department of Commerce, Bureau of the Census, Government Finances in 1960, Census of Population, 1960, Census of Manufactures, 1958, Statistical Abstract of the United States, 1961. U.S. Department of Agriculture, Agricultural Statistics, 1961. U.S. Department of the Interior, Minerals Yearbook, 1960. Authorization: for educational use.

case01.csv case01.R case01.wf1 case01.xlsx

Case 02 Home prices in Albuquerque: what determines home prices? (Economics, Real estate, Business)

Data reference: Albuquerque Board of Realtors. Authorization: for educational use.

case02.csv case02.R case02.wf1 case02.xlsx

Case 03 Taste of cheese: An assessment of subjective scores (Product development, Business)

Data reference: Moore, David S., and George P. McCabe (1989). Introduction to the Practice of Statistics. Authorization: for educational use.

case03.csv case03.R case03.wf1 case03.xlsx

Case 04 Consumption of soft drinks: Practicing categorical determinants (Consumer research). Data reference: Artificial data - Eray Yucel. Authorization: for educational use.

370 Multiple Linear Regression modeling - Analyzing demand for soft drinks.xlsx

case04.csv case04.R case04.wf1 case04.xlsx

Case 05 A promotion for soda consumers: The Linear Probability Model - simple and still useful (Business). Data reference: Artificial data - Eray Yucel. Authorization: for educational use.

case05.csv case05.R case05.wf1 case05.xlsx

Case 06 A demonstration of the effect of omitted variables (Simpson’s paradox). Data reference: Artificial data - Eray Yucel. Authorization: for educational use.

case06.csv case06.R case06.wf1 case06.xlsx

8.13 Frisch-Waugh-Lovell theorem (FWL theorem)

222 Handout 240508 - FWL theorem.pdf

222 Hw5 due DD MMM YYYY Day HH:MM Hw description

Exam Rules and Logistics

STUDENTS are responsible for every topic covered in class & recitations up to and including the last lecture/recitation prior to exam. Some previous exams with solution keys are available at Past materials (Folder).
PROCTORS are expected in FEASS A-108 15 minutes before the exam's start. Regarding the exchange of posts among PROCTORS, make sure Ms. Özlem Eraslan has been informed in a timely fashion. On the exam day only, directly call +905325435888 for emergencies.
STUDENTS are not to be admitted to exam without their STUDENT ID card or a live display of their 'SRS page + Citizen ID card / Passport'.
PROCTORS: Exam dates and times are as follows, where the STUDENTS are to be seated according to (221 (GSHEET)) & (222 (GSHEET))

ECON 221 Midterm 1: 31 October 2025 Friday 20:30 - 22:30

ECON 221 Midterm 2: 28 November 2025 Friday 21:00 - 23:00

ECON 221 Final: DD MMM YYYY, Day, HH:MM-HH:MM

◽ ◽ ◽◽◽◽◽◽◽◽◽◽◽

ECON 222 Midterm 1: 01 November 2025 Saturday 16:30 - 18:30

ECON 222 Midterm 2: 29 November 2025 Saturday 16:30 - 18:30

ECON 222 Final: DD MMM YYYY, Day, HH:MM-HH:MM

Exam duration is 75 minutes for Midterms & 105 minutes for Finals. STUDENTS are not allowed to leave the room in the first 30 minutes and not to be admitted after that.
There is no restroom allowance during the exam, except for the students with officially documented (by a Medical Committee ~ Tur: Heyet Raporu) chronic medical conditions. STUDENTS can leave only after they submit their work.
Books and notes are not allowed. Each STUDENT can use a formula sheet: two sides of a single A4-sized or smaller sheet. Formula sheets can contain anything. Formulas can be hand-written or computer-typed.
STUDENTS' use of standalone calculators is allowed. Use of other devices is not allowed.
Exchange of calculators, stationery and formula sheets between STUDENTS is not allowed.
STUDENTS will use pencils & erasers but not ink pens or roller pens. So, no scratching etc. is to be left on exam papers.
STUDENTS are not to use the back sides of exam sheets, responses on back sides are not to be graded, as back sides are not numbered, i.e., they are not pages.
STUDENTS are not to remove the staples of exam sets under any circumstances.
STUDENTS will not ask any questions during the exam. PROCTORS will not answer STUDENTS' questions of any sort. Every single word & term in the questions have been covered in the lectures. So, when the questions from STUDENTS like "I don't know the meaning of this word" are answered by PROCTORS, the answer may coincide with the response/solution seeked by the exam question, where correspondences as such may have legal consequences.
STUDENTS are not to leave the exam room without submitting their work and signing the attendance list.
By the end of the exam, PROCTORS are to dispose the unused exam sets, are to make sure that number of people on the attendance list and the number of exam papers submitted match. Upon the submission of exam papers and attendance lists to FEASS A-108 the exam-related duties end for PROCTORS.
Exam results are to be announced in two weeks' time after the exam date. Until then, no correspondences from STUDENTS regarding the exam are expected.

Google Sites

Report abuse