An  Introductory Probability Course

Why am I here?

Why take this course?

Introduction to Probability

An introduction to the various definitions of Probability

Random Experiments and Sample Spaces

A Sample Space is the space of possible outcomes of a random experiment

Probability Models

Probability Models and Events

Simple Random Samples Made Simpler

How simple can it get? A famous Scientist tells you.

Counting Techniques 1

How to Count (when sets are large)

counting techniques 2

Sets and Probabilty 1

Basic Set Theory and how it relates to Probability (Part 1)

Sets and Probability 2

Independent Events

When does the occurrence of one event have no effect on the probablities assigned to another?

Independent Events Examples

Conditional Probability

How do your probabilities change if you are told that an event B occurred?

The Talk show

Conditional Probability is everywhere!

Random Variables and Distributions

Random Variables and Distributions 2

Discrete Uniform and Hypergeometric

The uniform distribution obtains when you throw a fair die once. The Hypergeometric when you draw a random sample from a population with two types of individuals in it.

The Binomial Distribution

When you repeatedly toss a coin and count the number of heads in 20 tosses, this random variable has a binomial distribution

geometric series

Learn how to sum them!

Geometric and Negative Binomial

Two distributions obtained when you sample repeatedly until you get a fixed number of successes.

The Nose Job

Some really useful distributions applied to a bit of cosmetic surgery

Poisson Distribution

A Distribution for Count Data. The Number of raindrops on a part of a window pane.

The Poisson Process

A Model for Events or Points occurring randomly in time or space

Expected Value Part 1

The Expected Value is a Number indicating the "center" of the distribution of values of a random variable

Expected Value Part 2

Expected Values for Certain Distributions and the Laws for dealing with expected values

Variance of Distributions

The Variance is a measure of the spread or the variability in a random variable

Variances Part 2

Continuous Distributions

Distributions that can take any value in an interval, not just those in a discrete set.

Continuous Distributions 2

Transformations of Random Variables

Moments and the Continuous Uniform

Pond Z Investments

A Stat 230 Hedge Fund with guaranteed returns (guaranteed to be positive or negative)

The Exponential Distribution

One of the most important continuous distributions in applied probability

Computer Generated Random Variables

How does a computer generate random numbers from various distributions?

The Normal Distribution 1

The pre-eminent distribution in applied statistics

Normal Distribution II

The Ripov Casino

Expected value. What did you expect?

Multivariate Distributions

The Study of the joint distribution of two or more random variables that may be dependent

THE MULTINOMIAL

Multivariate Expected Values

measures_of_dependence.JPG

statistical measures of the dependence between two random variables

Indicator Random Variables

Random variables that take only two values, 0 or 1

Linear Combinations of Normal

When we take a linear combination of normal random variables the result is normally distributed

Normal Distribution approximations

The central limit theorem allows us to use the normal distribution for sums and averages

normal approximation 2

Normal approximations to Binomial, Poisson etc

normal approximation3

Normal Approximatons Part III

moment generating functions

a transform of distributions which permits determining distributions of sums