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HU Credits:
4
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Boris Begun
Coordinator Office Hours:
by appointment
Teaching Staff:
Dr. Boris Begun,
Prof Guy Ron,
Mr. Lavi Yair
Course/Module description:
A basic course in Probability an Statistics.
(The semester is split roughly equally between the Probability and Statistics parts.)
Course/Module aims:
To introduce the principal notions and tools of Probability Theory. To help students in developing Probabilistic Thinking.
To teach methods of analyzing and simulating experimental data. To show the confrontation of data with observation via parameter estimation, hypothesis testing, and prediction.
Learning outcomes - On successful completion of this module, students should be able to:
1. Explain and apply the basic concepts of probability, including conditional probability, Bayes’ Formula and the notion of independence.
2. Describe and apply the concepts of discrete and continuous random variables and probability distributions, including standard distributions such as binomial, geometric, Poisson, exponential, normal. Perform calculations involving jointly distributed random variables.
3. Interpret and apply two limit theorems – the Weak Law of Large Numbers and the Central Limit Theorem. Prove a version of the Weak Law of Large Numbers.
4. Conceptual and practical know-how of experimental/observational data analysis.
Attendance requirements(%):
Attendance recommended; not required
Teaching arrangement and method of instruction:
Weekly lectures + recitations
Course/Module Content:
-- SOME MODIFICATIONS POSSIBLE --
PART 1 - PROBABILITY
1. The notion of probability. Probability space. Elementary combinatorics and applications in symmetric probability spaces.
2. Notion of conditional probability, Law of total probability, Bayes' formula. Independence of two or more events. Bernoulli trials.
3. Notion of a random variable. Discrete and continuous random variables. Special distributions: binomial, geometric, Poisson, exponential. Distribution of a function of a random variable.
4. Notion of expectation. Properties of expectation. Expectation of a function of a random variable. Variance. Expectations and variances of special distributions.
5. Weak Law of Large Numbers.
6. Normal distribution and its properties.
7. Random vectors. Covariance. Correlation coefficient. Expectation of a function of several random variables. Distribution of a sum of independent random variables.
8. Central Limit Theorem. Normal approximation.
9. (time permitting) Conditional distribution. Law of total expectation.
PART 2 - STATISTICS
1. Review of important probability distributions in the framework of data analysis.
2. Statistical descriptions of data: Moments, correlations.
3. Uncertainties – statistical and systematic, and error propagation.
4. Preprocessing: denoising, smoothing.
5. Parameter estimation: R^2, Chi-square, log-likelihood, binned and unbinned.
6. Rudimentary Bayesian inference.
Required Reading:
N/A
Additional Reading Material:
Sheldon Ross: A first course in probability.
Louis Lyons: Statistics for Nuclear and Particle Physicists.
Course/Module evaluation:
End of year written/oral examination 75 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 25 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
Home assignments grade is a "magen" (can raise the final grade but cannot lower it).
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