Probability and Statistics
Instructor
Dr. Galit Ashkenazi-golan
Email :Galit.ashkenazi@gmail.com
Academic Year, Semesters
2018, spring semesters
Number of Hours/ Credits
3 hours lecture, 1 hour recitation
Mandatory/Elective
Mandatory
Prerequisites
Introduction to mathematics for physics
Course overview – short abstract
The course covers basic probability and statistics material. The students learn the classic (aximatic) approach to probability, combinatorics, conditional probability and concepts relating to random variables. In the part where Statistics is learned, the topics covered are point estimation, confidence interval and hypothesis testing.
Assessment: coursework and grade structure
Assignments – 7%
Final exams – 93%
Week-by-week content, assignments and reading
Week 1: The axioms of probability.
Week 2: Combinatorics, conditional probability –definition.
Week 3: Conditional probability: chain rule, Law of Total probability, Bayes’ rule.
Week 4: Random Variables – the discrete case.
Week 5: Random Variables – the continuous case.
Week 6: Expectation, variance and moment generating functions.
Week 7: Joint distributions – the discrete case.
Week 8: Joint distributions – the continuous case.
Week 9: Covariance, Pearson’s correlation coefficient.
Week 10: Law of large numbers, Central limit theorem.
Week 10: Point estimations: maximal likelihood estimators, unbiased estimators, MSE measurement.
Week 11: Confidence interval, hypothesis testing – type 1 and type 2 error, p-value.
Week 12: Testing hypothesis about mean of one population – known variance, unknown variance (t-test), and testing hypothesis about proportion (Z-test) and about variance (chi-square test).
Week 13: Testing hypothesis about two populations – paired and independent samples, test for equal variances (F-test) , test for independence and goodness of fit (chi-square test).
Required text – in language of origin (if Hebrew or Arabic, no need to translate it)
קורס ראשון בהסתברות, שלדון רוס, הוצאת האוניברסיטה הפתוחה.