Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing.
Ongoing course
Time: M-F 11:10 AM – 12:45 PM
Location: HUMN 1B70
Office hours: Click here
Grading
Homework: 25% – Weekly homework (you must turn them in)
Participation 20%
Midterm I (06/10): 25%
Final (to be announced) : 30%
Textbook
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Course notes
Limit Theorems in Probability Theory – MATH 3510 – SUMMER
The Law of Large Numbers and the Central Limit Theorem
Normal Distrubtion – MATH 3510 – SUMMER
Gaussian curve, properties of the normal distribution
Exponential Distribution – MATH 3510 – SUMMER
Continuous distributions, exponential distribuition
Binomial Distribution – MATH 3510 – SUMMER
Introduction to distributions, binomial distribution
Expected Value – MATH 3510 – SUMMER
Expected Value, Expected value of functions of random variables and other formulas.
Bayes’s formulas and Independence of Events – MATH 3510 – SUMMER
Bayes’s formulas and Independence of Events. The Monty Hall Dilemma
Introduction to conditional probability – MATH 3510 – SUMMER
Conditional probabilities
Sample Spaces, Events and Kolmogorov’s axioms – MATH 3510 – SUMMER
Sample spaces, events, axioms of probability.
Other Counting Principles – MATH 3510 – SUMMER
Addition and Subtraction principles and the Inclusion-exclusion formula.
Equally Likely Outcomes and Counting Principles – MATH 3510 – SUMMER
Defining probability for random experiment with equally likely outcomes. Counting principles.
Introduction to the Course – MATH 3510 – SUMMER
Comment about the course and discussion about probability of events
Rodrigo Ribeiro, Ph.D 