Summary of Topics and Examples from Chapter 1

1. Components of a probability experiment: Sample spaces (discrete vs. continuous), events, elementary outcomes

i. From class: Two network routers (discrete); time to access a webpage (continuous)

ii. From Homework: HW1 #3

iii. Hofmann: 1.9 #2

2. Events in Set Notation and Venn Diagrams

i. From class: Network routers and accessing the webpage

ii. From Homework: HW1, #4, HW2 #2,#3

iii. Hofmann 1.9 #3, #7

iv. Extra Exercises for HW 3: Morning Activities

3. Kolmogorov’s Axioms and Consequences

i. From class: Dial-up connection to AOL

ii. From Homework: HW 2 #1, #5 (a)

iii. Hofmann 1.9 #7

iv. Baron Examples: 2.10, 2.11, 2.13, 2.14, 2.28

4. Probability Models for Equally Likely Outcomes

i. From class: octal numbers, toss a coin – how many sequences are possible?, pizza toppings, lottery, coin toss – how many ways to get x heads?

ii. From HW: HW2 #4, practice counting

iii. Extra exercises for HW 3: 2x2 tables, exact change, randomized experiment

iv. Hand-outs: Multinomial and acceptance sampling

v. Hofmann: 1.9 #4, #6 vi. Baron Examples: 2.19, 2.24, 2.25-2.27

5. Conditional Probability

i. From class: Box with defective and good chips, three colored cards

ii. From homework: HW1 #4 (e), (f); HW 2 Best by

iii. Hofmann: 1.9 #7

iv. Baron Examples: 2.28, 2.29-2.30

6. Independence

i. From class: AOL network (version 2), parallel systems and series systems with independent components

ii. From homework: HW2 #3, HW3 #1, #5

iii. Hofmann: 1.9 # 11

iv. Baron Examples: 2.17

7. Law of Total Probability and Bayes’ Rule:

i. From class: gold coins and pennies, medical test

ii. HW 3: #2, #3

iii. Extra exercises for HW 3: Measurement Error in the NRI

iv. Hofmann: Forensics example in text, 1.9 #8, #12, #13, #14, #17

v. Baron Examples: 2.31-2.32

8. Bernoulli Experiments and R.V.’s

i. From class: Darts

ii. From Homework: HW 3 #5