1 Objectives

The students finishing the course must have acquired the necessary knowledge about the following topics:

1. Basic Probability Theory.
2. Univariate random variables.
3. Expected Values.
4. Multivariate random variables (random vectors).
5. Expected Values of Functions of Random Vectors.
   
6. Special Random Variables and Repeated Sampling Distributions.

2 Outline and Exercises

• Basic Probability Theory (Exercises) (Answers)
• Univariate Random Variables (Exercises) (Answers)
• Expected Values (Exercises) (Answers)
• Random Vectors (Exercises) (Answers)
• Expected Values of Functions of Random Vectors (Exercises) (Answers)
• Special Random Variables and Repeated Sampling Distributions (Exercises) (Answers)

3 Exam

The final grade on a scale of 0 to 20 is awarded based on two written exams:

1. Midterm Exam: counts \(50\%\) (duration 1 hour).

Covers the following material:

1. Basic Probability Theory.
2. Univariate random variables.
3. Expected Values.
4. Multivariate random variables (random vectors).

The grade for this exam is between 0 and 10.

2. Normal Exam: counts \(50\%\) (duration 1 hour).

Covers the following material:

5. Expected Values of Functions of Random Vectors. 6a. Special Random Variables. 6b. Repeated Sampling Distributions.

The grade for this exam is also between 0 and 10.

The final grade is the sum of the result of midterm exam and the result of the normal exam (grade between 0 and 20). You pass the exam if the final grade is at least \(9.5\) out of \(20\).

3. Resit Exam: counts \(100\%\) (duration 2 hours).

This exam is for students that did not manage to pass the course by means of the midterm exam and the normal exam (or want to improve their grade). This exam covers all the material of the course. You pass the exam if your grade for this resit exam is at least \(9.5\) out of \(20\).

4 Example Exam

• Example Exam with Answers
• You can use the first part as an example midterm-exam.
• You can use the second part as an example Normal-exam.
• You can use the whole exam as an example Resit-exam.

5 Bibliography

The lecture notes contain all the material to be discussed in the course. If you need more information, you can consult the following literature:

• Miller & Miller, John E. , Freund’s Mathematical Statistics with applications , 8th Edition, Pearson Education, [MM], , 2013
• P. Newbold, W. Carlson, B. Thorne, , Statistics for Business and Economics , 8th Edition, Pearson Education, [N], , 2012