Math 309 Probability—Fall 2015: Study Sheet for Test 1
Test questions will come primarily from examples in classroom presentations and homework problems;
so, with the exception of serial and parallel systems, all questions should come from material in the
assigned chapters of Finan’s text).
Text Section—Finan
Homework Problems
1.Set definitions: equal sets; cardinality; empty set; subset; proper
HW1: 1, 2
subset; power set; power set proof by mathematical induction
2.Set operations: complement; union; intersection; Venn diagrams;
HW1: 3, 4
disjoint sets; DeMorgan’s laws; Inclusion-exclusion principle; Cartesian
product
3.Fundamental principle of counting: tree diagrams; Fundamental
HW2
theorem of counting
4. Permutations:
HW2
5. Combinations: mathematical induction again and binomial theorem
HW2, HW3
Old 5. with indistinguishable objects: multinomial theorem
Simple problem
6.Definitions of probability: axioms, equally likely principle, birthday
HW4
problem (example 6.7)
7.Properties of probability: probability of union, intersection
HW5
8.Probability and counting (trees): multiplication rules for probability
HW5
trees
9.Conditional probability:
HW6
10.Bayes formula: understand equation (10.1) and Bayes formula (Thm
HW6
10.1)
11.Independent events: independence, pairwise independence, mutual
HW5, HW7
independence; parallel and serial systems
12. Odds and conditional probability
Assigned reading: F: p. 97:
problems 12.2, 12.4
13.Discrete r.v.s: random variables; discrete r.v.s
F, p. 104: problem 13.7
14.Pmf, cdf: given a cdf, find a pmf and vice versa; indicator variable
F, p. 110: example 14.6; p.
112: problem 14.8