Assigned Reading

Although our text does not conduct a formal probability review, it would be advised that you consult your prerequisite course's probability textbook. The free, online Khan Academy also has a nice collection of short probability and statistics tutorials covering a wide variety to topics applicable to this course.

Useful Equations

Rules of Integration

Chain Rule for Integration

If  , 

Rules of Differentiation

, 

Chain Rule for Differentiation

Laws for Probabilities of Events

Venn Diagram

Law of Addition

Definition of Conditional Probability

Bayes' Rule

Random Variables

Conditional Probability

Conditional Expectation

Computing Expectations by Conditioning

Integer Series Identities

Combinations of Choosing k from n Elements

Frequently Used Random Variables

Exponential Continuous Random Variable

RV X with parameter α > 0.

Supports [0, ∞)

Uniform Continuous Random Variable

RV X.

Supports [a, b]

Bernoulli Discrete Random Variable

RV X with parameter 0 < p < 1.

Supports k = {0, 1} 

Binomial Discrete Random Variable

RV X with parameters integer n > 0, 0 < p < 1.

Supports k = {0, 1, ..., n} 

Geometric Discrete Random Variable

RV X with parameter 0 < p < 1 indicating the probability of success.

The number X of Bernoilli trials needed to get one success, supported on the set k = {1, 2, ...}.

The number of Y = X - 1 failures before the first success, supported on the set k = {0, 1, ...}.

Poisson Discrete Random Variable

RV X with parameter λ > 0.

Supports k = {0, 1, ...}