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

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 (RVs)

Conditional Probability

If X and Y are discrete RVs, the definition of conditional probability for all values of y such that Pr(Y = y) > 0 is

If X and Y are continuous RVs and have joint PDF f_XY(x,y), then the conditional PDF for all values of y such that f_Y(y) > 0 is

For RV X, we can find Pr(X <= x) by conditioning on RV Y. If Y is a discrete RV, then

If Y is a continuous RV with desity f_Y(y), then

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, ...}