Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits
Textbook
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Course notes
Central Limit Theorem – MATH 4510/5510
Central Limit Theorem and little about histograms
The Law of Large Numbers – MATH 4510/5510
The Law of the large numbers: statement, proof and how to use it
Independent Random Variables – MATH 4510/5510
Introduction to independence for random variables
The Joint Cumulative Distribution – MATH 4510/5510
Introduction to joint distributions
Review for Midterm II – MATH 4510/5510
Review of all important concepts for the Midterm II
The Continuous Uniform Random Variable – MATH 4510/5510
Definition and properties of uniformly distribution random variables over intervals
Continuous Random Variables – MATH 4510/5510
Introduction to Continuous Random Variables
How to prepare for Midterm II and other comments – MATH 4510/5510
Tips and comments about Midterm II
The Cumulative Distribution Function – MATH 4510/5510
The Cumulative Distribution Function and some properties
Binomial Distribution – MATH 4510/5510
One of the most important discrete distributions
Variance and Standard deviation – MATH 4510/5510
Introduction to variance and standard deviation
Expected Value of Sums of Random Variables – MATH 4510/5510
Expected value of sums of random variables and the substitution formula
Expected value and Investments – MATH 4510/5510
Building a mathematical model to understand the impacts of deviating too much from the expected value
Expected value of a function of a random variable – MATH 4510/5510
Formula to compute expected value of a function of a random variable
Expected Value – MATH 4510/5510
Expected value of discrete random variables and connection with Law of Large Numbers
Random Variables – MATH 4510/5510
General definition of random variables and examples in the discrete case
Monty Hall Dilemma – MATH 4510/5510
Solving and discussing the famous Monty Hall dilemma
The m points problem – MATH 4510/5510
An Important historical problem involving probability theory
The Conditional Measure – MATH 4510/5510
Investigating the conditional probability and an example from genetics
Conditional Probability – Part II – MATH 4510/5510
Introduction to conditional probability
Conditional Probability – Part I – MATH 4510/5510
Introduction to conditional probability
Midterm I – Review I – MATH 4510/5510
Comments about Midterm I and theoretical review
Probability as a measure of belief – MATH 4510/5510
Probability as a measure of belief
Probability measure as a continuous set function – MATH 4510/5510
Probability measure as a continuous set function. Increasing and decreasing events.
Sample spaces with equally likely outcomes – MATH 4510/5510
Sample spaces with equally likely outcomes
Basic Principle of Counting – MATH 4510/5510
(Generalized) Basic Principle of Counting and Permutations
Introduction to the course – MATH 4510/5510
General comments about probability theory and our course!
