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.

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Course notes

## 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

## 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

## 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

## 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

## 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

## Law of Large Numbers and Simulations – MATH 3510

Comments on Law of Large Numbers and simulations

## Introduction to the course – MATH 3510

General comments about probability theory and our course!