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HU Credits:
3
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Boris Begun
Coordinator Office Hours:
by appointment
Teaching Staff:
Dr. Boris Begun
Mr. Tsvika Lakretz
Course/Module description:
A basic course in Probability Theory.
Course/Module aims:
To introduce the principal notions and tools of Probability Theory. To help students in developing Probablistic Thinking.
Learning outcomes - On successful completion of this module, students should be able to:
1. Explain and apply the concepts of basic probability, including conditional probability, Bayes’ Formula and the notion of independence of two or more events.
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.
3. Perform calculations involving jointly distributed random variables.
4. Interpret and apply two limit theorems – the Weak Law of Large Numbers and the Central Limit Theorem.
Attendance requirements(%):
Attendance recommended; not required
Teaching arrangement and method of instruction:
Weekly lecture + recitation
Course/Module Content:
1. Axiomatic approach to the notion of probability. Probability space. Symmetric and non-symmetric probability spaces.
2. Elementary combinatorics and applications in symmetric probability spaces – samples with and without replacement.
3. Notion of conditional probability: definition and examples. Law of total probability. Bayes' formula. Notion of independence of two events, and its connection with conditional probability.
4. General notion of independence. Sequence of independent trials.
5. Notion of a random variable. Discrete random variables. Probability mass function.
6. Special discrete distributions: binomial, geometric, Poisson.
7. Notion of expectation. Properties of expectation. Expectation of a function of a random variable.
8. Variance.
9. Continuous random variables. Probability density function and cumulative distribution function.
Special continuous distributions: uniform, exponential.
10. Weak Law of Large Numbers.
11. Normal distribution and its properties. Standard normal distribution table.
12. Random vectors. Covariance. Correlation coefficient. Expectation of a function of several random variables. Distribution of a sum of independent random variables. Conditional distribution. Law of total expectation.
13. Central Limit Theorem. Normal approximation.
14. (time permitting) Poisson flow of events.
Required Reading:
N/A
Additional Reading Material:
Sheldon Ross: A first course in probability.
Grading Scheme :
Additional information:
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