MAT 526 Review Problems
1. Give precise definitions of the following;
(a) X is a Poisson random variable with parameter .
(b) cfw_Xt , t 0 is a Poisson process with intensity (rate) .
(c) cfw_Xn , n = 0, 1, 2, . . . is a Markov chain with transition matr
Name:
Version:
LSSGB Test 2
1.3
1)Repetition and Replication help the Six Sigma team in determining:
SELECT THE CORRECT ANSWER
A.
B.
C.
D.
Short term variability
Long term variability
All of the above
None of the above
Ans: C
2)For 5 factors and 2 levels,
Name:
Version:
LSSGB Test 1 with Answers
1.3
1) The difference between strategic quality goals and the strategic business
plan is that:
SELECT THE CORRECT ANSWER
A.
B.
C.
D.
Strategic quality goals are often a lower tier than the strategic business plan
T
MATH 392 Topics in Mathematical Economics
Topic 4 Voting methods with more than 2 alternatives
4.1 Social choice procedures
4.2 Analysis of voting methods
4.3 Arrows Impossibility Theorem
4.4 Comparison voting methods
1
4.1
Social Choice Procedures
A gro
Undergraduate Senior Thesis
University of Washington
Voting Theory and Banzhaf
Vectors
Author:
Natalie Hobson
Supervisor:
Professor Sara Billey
Abstract
This paper gives a general description of voting theory and looks specifically at
problems relating to
Math 017 Lecture Notes
(1.1)
Preference Ballots and Schedules
Election ingredients:

Set of choices/candidates to choose from
Voters whom make these choices
Ballots lets voters designate their choices
(vote on something): ski/snowboard/other (both ways)
9/2015
Snapsho t s o f m o d e r n m athematics
from Ob e r wo l f a c h
How to choose a winner : the
mathematics of social choice
Victor ia Powers
Suppose a group of individuals wish to choose among
several options, for example electing one of several
c
M ATH 1340: Mathematics and Politics
Summer 2010
Homework 4 solutions
ASSIGNMENT: exercises 2, 3, 4, 8, and 17 in Chapter 2, (pp. 6568).
Solution to Exercise 2.
A coalition that has exactly 12 votes is winning because it meets the quota. This coalition
is
Math13 HW 6 Chapter 10
1. If a voting system has three or more alternatives, satisfies the Pareto condition, always produces a
unique winner, and is not a dictatorship, what conclusion follows from the GS theorem?
2. Are there voting methods that are neve
1
4] VOTING SYSTEMS (Part Three):
SOME SHORTCOMINGS OF kALTERNATIVE SYSTEMS; k>2
4.1) Name at least five desirable properties that kAlternative Voting
Systems, k > 2, should satisfy.
4.2) State the Condorcet Winner Criterion (CWC). (Page 292)
4.3) Show
In many actual voting situations, the principal one person one vote
is not justified. For example,
At a company shareholders meeting, the number of votes a
person has corresponds to the number of shares owned.
In a law firm, a senior partner usually has m
WHICH METHODS SATISFY OR VIOLATE WHICH CRITERIA?
Recall that the four fairness criteria are majority, Condorcet, monotonicity, and independence of irrelevant alternatives. Also recall that for a method to satisfy a fairness criterion,
every possible elect
Chapter 4: Probability The Study of Randomness
4.1: Randomness
4.2: Probability Models
4.3: Random Variables
4.4: Means and Variances of Random Variables
4.5: General Probability Rules
4.1: Randomness
A phenomenon is random if individual outcomes are
unce
4.4: Means and Variances of Random Variables
Example 2: Compare the means of the random variables X and Y :
X
Probability
2
0.4
3
0.6
Y = 2X
Probability
4
0.4
6
0.6
4.4: Means and Variances of Random Variables
Example 3: Linda is a sales associate at an a
4.3: Random Variables
How do we assign probabilities to events involving a continuous
random variable X ?
Example: Let X be the amount of time (in minutes) that you will
have to wait for a friend who will be at most 15 minutes late.
Then, X is a continuou
Chapter 4: Probability The Study of Randomness
4.1: Randomness
4.2: Probability Models
4.3: Random Variables
4.4: Means and Variances of Random Variables
4.5: General Probability Rules
4.5: General Probability Rules
Objectives
Venn diagrams
General additi
4.5: General Probability Rules
Conditional Probability
Notation: P(AB) = the probability of A given that event B has
occurred.
P(AB) =
number of outcomes in A and B
number of outcomes in B
Example 1: Consider the current U.S. Senate membership:
Female
M
4.5: General Probability Rules
Recall: Events A and B are independent if they have no influence
on each others occurrence.
If A and B are independent, then P(A and B) = P(A)P(B).
If A and B are independent, then P(BA) = P(B).
Example: Supposed two dice a
4.4: Means and Variances of Random Variables
Mean of a Continuous Random Variable
Recall: The probability distribution of continuous random variables
is described by a density curve.
The mean lies at the center of symmetric density curves such
as the norm
MAT 221  Fall 2016
Formulae
If X is a discrete random variable taking on values x1 , . . . , xk with respective probabilities
p1 , . . . , pk , then the mean is X = x1 p1 + + xk pk , the variance is
q
2
2 .
X
= (x1 X )2 p1 + + (xk X )2 pk , and the stan
4.2: Probability Models
Exercise 4.29:
Exercise 4.30:
Ex 3: Suppose two people are randomly selected from the world
population. Let E be the event that both of these people live in
Europe. Which of the following events is Ec ?
(a) The event that neither o
MAT 532 HOMEWORK 1.5
DUE TUESDAY
13 SEPTEMBER 2016 AT THE BEGINNING OF CLASS
1. (a) Using 3digit floating point arithmetic, apply Gaussian elimination (without partial
pivoting) to solve the following system.
"
103 1
2
3
2
44
#
.
Dont solve with backsub
MAT 532 HOMEWORK 3.10
DUE TUESSDAY
25 OCTOBER 2016 AT THE BEGINNING OF CLASS
1. Let
1
4
5
A=
4 18 26 .
3 16 30
(a) Find the LU factorization of A .
(b) Use your LU factorization to solve Ax = b, where b =
(c) Use your LU factorization to determine A
1
h
6
MAT 532 HOMEWORK 1.6
DUE THURSDAY
15 SEPTEMBER 2016 AT THE BEGINNING OF CLASS
1. Use geometry to decide which of the following three linear systems is worstconditioned
and which is bestconditioned. Explain your answer.
(
1.001 x
y = .235
x + .0001 y =
MAT 532 HOMEWORK 1.4
DUE THURSDAY
8 SEPTEMBER 2016 AT THE BEGINNING OF CLASS
1. (a) Set up the linear system to approximate a solution to the boundary value problem
y00 ( t) = kt
on the interval [0, 1], with boundary conditions y(0) = 1 and y(1) = 0, usin
MAT 532 HOMEWORK 1.2, 1.3
DUE TUESDAY
6 SEPTEMBER 2016 AT THE BEGINNING OF CLASS
1. Use Gaussian elimination with backsubstitution to solve the system. You should apply the algorithm as discussed in class; full credit will be given only for complete full
MAT 532 HOMEWORK 3.10
DUE TUESDAY
25 OCTOBER 2016 AT THE BEGINNING OF CLASS
1. Let
1
1
3
12
1 2 8
.
1 1
4 16
A=
1
(a) Find a nonsingular matrix P such that P A is the RREF of A .
(b) Find nonsingular matrices P and Q such that P AQ is the rank normal form