Notes for STAT3320
Preface
1
Probability and counting
1.1
Theoretical Notes
1.1.1
Definition 1.2.1 (Sample space and event).
1.1.2
De Morgan’s laws
1.1.3
Naive Definition of Probability
1.1.4
Multiplication rule
1.1.5
Permutation
1.1.6
Combination
1.1.7
Adjustment of overcounting
1.1.8
Binomial coefficient
1.1.9
Binomial theorem
1.1.10
Sampling with replacement
1.1.11
Sampling without replacement
1.1.12
General definition of probability
1.1.13
Properties of probability
1.2
Examples
1.2.1
Example 1.2.2 (Coin flips).
1.2.2
Example 1.2.3 (Pick a card, any card).
1.2.3
Example 1.4.3 (Runners).
1.2.4
Example 1.4.5 (Ice cream cones)
1.2.5
Example 1.4.6 (Subsets).
1.2.6
Example 1.4.10 (Birthday problem)
1.2.7
Example 1.4.12 (Leibniz’s mistake).
1.2.8
Example 1.4.13 (Committees and teams).
1.2.9
Example 1.4.17 (Club officers)
1.2.10
Example 1.4.18 (Permutations of a word)
1.2.11
Example 1.4.20 (Full house in poker)
1.2.12
Example 1.4.21 (Newton-Pepys problem)
1.2.13
Example 1.4.22 (Bose-Einstein)
1.2.14
Example 1.5.1 (Choosing the complement).
1.2.15
Example 1.5.2 (The team captain).
1.2.16
Example 1.5.3 (Vandermonde’s identity).
1.2.17
Example 1.5.4 (Partnerships).
1.2.18
Example 1.6.4 (de Montmort’s matching problem).
2
Ch. 2: Conditional Probability
2.1
Theoretical Notes
2.1.1
Conditional probability.
2.1.2
Bayes’ rule
2.1.3
Odds
2.1.4
Law of total probability (LOTP).
2.1.5
Conditional probabilities are probabilities
2.1.6
Independence of events
2.2
Examples
2.2.1
Example 2.2.2 (Two cards).
2.2.2
Example 2.2.5 (Two children).
2.2.3
Example 2.2.6 (Random child is a girl)
2.2.4
Example 2.2.7 (A girl born in winter).
2.2.5
Example 2.3.7 (Random coin).
2.2.6
Example 2.3.9 (Testing for a rare disease).
2.2.7
Example 2.3.10 (Six-fingered man).
2.2.8
Example 2.4.4 (Random coin, continued).
2.2.9
Example 2.4.5 (Unanimous agreement).
2.2.10
Example 2.5.9 (Conditional independence doesn’t imply independence).
2.2.11
Example 2.5.10 (Independence doesn’t imply conditional independence).
2.2.12
Example 2.5.11 (Conditional independence given
\(E\)
vs. given
\(E^c\)
).
2.2.13
Example 2.5.12. (Why is the baby crying?)
2.2.14
Example 2.6.1 (Testing for a rare disease, continued).
2.2.15
Example 2.7.1 (Monty Hall).
2.2.16
Example 2.7.2 (Branching process).
2.2.17
Example 2.7.3 (Gambler’s ruin).
2.2.18
Pitfalls and paradoxes
2.2.19
Biohazard 2.8.1 (Prosecutor’s fallacy).
2.2.20
Example 2.8.2 (Defense attorney’s fallacy).
2.2.21
Example 2.8.3 (Simpson’s paradox).
2.2.22
Simpson’s paradox
3
Appendix
3.1
Common discrete distributions
3.2
Common continuous distributions
3.3
Table of standard normal distribution
3.3.1
Confidence Interval Critical Values,
\(z_{α/2}\)
3.3.2
Hypothesis Testing Critical Values
3.4
Table of
\(t\)
-critical values
References
Published with bookdown
Handbook of STAT3330
References
Joseph K. Blitzstein, Jessica Hwang. 2019.
Introduction to Probability
. 2nd ed. Chapman; Hall/CRC.