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STAT 3743 Daily Outline

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2010-09-20 Mon

Selecting ordered samples

examples

Selecting unordered samples

More about binomial coefficients, Pascal's triangle

Birthday problem

Poker hands

royal flush
four of a kind

Conditional probability

Example: draw 2 cards, without replacement

Definition

Example: toss a coin twice

Example: toss a die twice

A = {outcomes match}
B = {sum of outcomes >= 8}

Properties

P(B|A) nonnegative
P(S|A) = 1
cond. prob of disjoint union is sum of cond. probs

More properties

Multiplication rule: P(A and B) = P(A)*P(B|A)

Mult. rule for several events

Examples

Good example: transferred ball

Independence

Example: toss two coins

Definition, intuition

Proposition: A, B independent then so are complements

Mutual Independence

Example: toss 100 coins

Pairwise doesn't imply mutual

Example: computers in series

Bayes' Rule

The theorem

Picture

What does it mean?

Author: G. Jay Kerns <gkerns@ysu.edu>

Date: 2010-10-08 15:18:47 EDT

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