Intro. Probability and Statistics – MATH 3510

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.

Textbook

Understanding Probability

by Henk Tijms

Other books I like

Course notes

Final Review

Central Limit Theorem – MATH 3510

Central Limit Theorem and histograms

Normal curve

Continuous Random Variables – MATH 3510

Definition of continuous random variables, probability density functions

Independent Random Variables – MATH 3510

Introduction and useful properties of independent random variables

Midterm II – Review II – MATH 3510

Second review for our Midterm II

Midterm II – Review I – MATH 3510

First review for our Midterm II

Variance and Standard Deviation – MATH 3510

Definition of Variance, Standard deviation. Chebyshev’s Inequality

Can we trust the expected value? – MATH 3510

Exploring a concrete situation involving expected values and investments

Expected Value of Sums of Random Variables – MATH 3510

Computing expected value of sums of random variables and another formula compute expectations

Independence of Events – MATH 3510

Formal definition of independent events and examples

Bayes’ Formulas – MATH 3510

Bayes’ Formulas and application on insurance

Monty Hall Dilemma – MATH 3510

Using conditional probabilities to formalize the solution of the famous Monty Hall Dilemma

Conditional Probability – II – MATH 3510

Introduction to conditional probabilities – Part II

Conditional Probability – MATH 3510

Introduction to conditional probabilities

Continuity of Probability Measure – MATH 3510

Continuity of probability measure: increasing and decreasing sequences of events

Extending Axioms of Probability – MATH 3510

Extending the axioms of probability to sample spaces with infinitely many outcomes

Using Probability Distributions: exercises – MATH 3510

Some exercises whose solutions are made easier if you use some well-known probability distributions

Study Guide: Probability Distributions – MATH 3510

A study guide about the most important probability distributions and how to use them

Hypergeometric Distribution – MATH 3510

Introduction to the Hypergeometric Distribution

Poisson Distribution – MATH 3510

Introduction to the Poisson Distribution

Binomial Distribution: concrete problem – MATH 3510

Modeling concrete problems with binomial distributions

Binomial Distribution – MATH 3510

Introduction to the most important discrete distribution

Sample Space with equally likely outcomes – MATH 3510

Formulas and examples when we have a sample space with equally likely outcomes

Combinations

Basic principle of counting – MATH 3510

Basic principle of counting and permutations

Expected Value: discrete case – MATH 3510

Expected Value of Discrete Random Variables

Random Variables

Basic Concepts of Probability – MATH 3510

Basic Concepts of Probability

Law of Large Numbers and Simulations – MATH 3510

Comments on Law of Large Numbers and simulations