# Intro. Probability and Statistics – MATH 3510 – SUMMER

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

Homework: 25% – Weekly homework (you must turn them in)
Participation 20%
Midterm I (06/10): 25%
Final (to be announced) : 30%

Homework sets

Second week assignment – due to 06/10 – set of exercises is on Canvas

First Week Assignment – Due to 06/03

Textbook

## Understanding Probability

by Henk Tijms

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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

## Geometric Distribution – MATH 3510 – SUMMER

Geometric distribution

## Poisson Distribution – MATH 3510 – SUMMER

Poisson distribution

## Binomial Distribution – MATH 3510 – SUMMER

Introduction to distributions, binomial distribution

## Variance – MATH 3510 – SUMMER

Introduction to variance

## Expected Value – MATH 3510 – SUMMER

Expected Value, Expected value of functions of random variables and other formulas.

## Discrete Random Variables – MATH 3510 – SUMMER

Random variables and independence

## 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.