Webpage of the probability and statistics tutorials. By Lluís Sabater.
We will use Postal Owl to submit the homework and grades. Therefore, you should enroll the course in Postal Owl.
As it is said in the Lecture Page:
"There will be two written in-class tests for a total of 100 points (50 for each test). To get the zápočet the sum of your test scores must be 50 or greater. Attendance of regular tutorials is not mandatory."
Dates of the tests: 8th April, 20th May.
The first test will cover the topics of the first 6 weeks. Discrete probability.
The second test will cover the rest of the topics of the Tutorials (7-11 weeks). The structure will be similar to the first test.
Homework will be classified by the following cathegories:
*: Mechanical problems (solvable just applying the definitions)
**: Normal problem (requires some easy thinking)
***: Requires a bit more of effort
?: The solution of the problem can be checked in some place (e.g. wikipedia), so the task is to look at that place.
(There can be new labels in the future). Each week the homework will be grouped by cathegories: [* A,B,C] means that the problems A, B and C are cathegory * problems.
About Conditional probability: chain rule, the law of total probability, Bayes theorem and its interpretation.
Problems Covered: 3, 4, 5, 6. (12,14)
(12, 14 are 9 and 10 from the previous week).
We also covered problem 8 from previous week set.
Independent events and discrete random variables.
Problems Covered: 1, 4, 6, 7.
We also covered problem 7 from previous week set.
Expectation. Linearity and Conditional expectaion
Problems Covered: 1, 3, 5, 6, 7.
We also covered problem 11 from previous week set.
Variance. Joint distribution, convolution.
Problems Covered: 1, 3, 4, 7.
We also covered problem 10 from previous week set.
Continuous random variables: pushforward measure, probability density function, cumulative distribution function.
Problems Covered: 1, 3, 5, 6, 9.
We also covered problem 9 and 10 from previous week set.
Continuous random variables: joint distribution and independence, convolution formula for continous rv's.
Problems Covered: 2, 5, 7a.
We also commented the problems of last week's test.
The Markov and Chebyshev inequalities. The central limit theorem
Problems Covered: 1, 2, 3.
We also covered problem 7 from previous week set.
Introduction to Statistics. Estimators and their properties (bias and consistency). Mean square error.
Problems Covered: 1, 4, 6.
Method of moments and Maximum likelihood estimators.
Problems Covered: 1, 3, 4.
Hypothesis Testing and Linear regression.
This is a new Problem set with the last topics of the subject.
Week 3:
Problem Set 2.About Conditional probability: chain rule, the law of total probability, Bayes theorem and its interpretation.
Voluntary Homework: [* 11], [** 2], [*** 13], [? 9,10]
Week 4:
Problem Set 3.Independent events and discrete random variables.
Voluntary Homework: [* 2,9], [** 3,8], [? 11]
Week 5:
Problem Set 4.Expectation. Linearity and Conditional expectaion.
Voluntary Homework: [* 8], [** 9,11], [? 10]
Week 6:
Problem Set 5.Variance. Joint distribution, convolution.
Voluntary Homework: [* 5,6,9,10], [** 7d], [*** 12], [? 11]
Week 7:
Problem Set 6.Continuous random variables: pushforward measure, probability density function, cumulative distribution function.
Voluntary Homework: [* 11], [** 4], [*** 7]
Week 8:
Problem Set 7.Continuous random variables: joint distribution and independence, convolution formula for continous rv's.
Voluntary Homework: [* 3,4], [** 8,9], [*** 10], [? 11]
Week 9:
Problem Set 8.The Markov and Chebyshev inequalities. The central limit theorem
Voluntary Homework: [* 4, 6], [** 5, 8]
Week 10:
Problem Set 9.Introduction to Statistics. Estimators and their properties (bias and consistency). Mean square error.
Voluntary Homework: [* 2], [** 3, 5]
Week 11:
Problem Set 10.Method of moments and Maximum likelihood estimators.
Voluntary Homework: [* 2], [** 6, 7]
Hypothesis Testing and Linear regression.
This is a new Problem set with the last topics of the subject.