Take Notes
International & Global Studies
172/180
58/70
340/420
570/670
85.0 B
Micro Economics
34/41
24/40
58/81
70.0 C
Media & the Sexes
114.5/120
79/90
67/80
260.5/290
.89B
2
NONDISCLOSURE AGREEMENT
This Nondisclosure Agreement (this Agreement), dated effective as of the date signed by parties
below (the Effective Date) is between WoTaBu Intl., Inc. (WoTaBu Intl.) and the person whose signature
appears at the end of this Agree
Situational/SWOT Analysis
While conducting a PEST analysis for World Wide Eats, we will look at the strengths,
weaknesses, opportunities, and threats in our restaurant.
Strengths:
o Variety: World Wide Eats will have much more variety than anywhere in the
Chris Carroll
Planning Project
12/1/15
Asheville, North Carolina is a city in Buncombe county and it is the largest city in
Western North Carolina, and that also makes it the 11th largest city in the state. Besides being a
fairly large city it is also a v
Chris Carroll
1/19/16
World Ecology Problems
I was pretty surprised by my footprint because I thought that I treated the environment a lot
better than I actually do according to my score since I got an 88. I can change some of the things
I do on a daily b
Situational/SWOT Analysis
While conducting a PEST analysis for World Wide Eats, we will look at the strengths,
weaknesses, opportunities, and threats in our restaurant.
Strengths:
o Variety: World Wide Eats will have much more variety than anywhere in the
Chris Carroll
World Ecology Problems
Planet in Peril Part 1
4/19/16
Planet in Peril is a documentary about a full year long investigation to study things that
are causing huge problems including climate change, deforestation, overpopulation, species loss
Bryan Jones Portals Past

For this piece, I chose Formalist Criticism I feel that this piece was too simple in a
way. Formalist Criticism is criticism on an art piece that deals with elements of art
and principles of design. There was not much happening
S6880 #15
Optimization and Root Finding
Optimization and Root Finding
In statistics, often arises in maximum likelihood problem:
i.i.d.
Data : x1 , . . . , xn f (x), x = (x1 , . . . , xn )t
n
Likelihood L(x) =
f (xi ) as a function of .
i =1
Need to ma
S6880 #16
Introduction to Resampling Procedures
Jackknife and Bootstrap
Introduction
For X F , X1 , . . . , Xn sampled from X . Want to estimate , a
parameter depending on F . = (F ). Examples:
(F ) = mean =
xdF (x ),
(F ) = variance =
x 2 dF (x ) [ xdF (
S6880 #14
Variance Reduction Methods #2: Buffons Needle
Experiment
Buffons Needle Experiment
Original Form
The goal of the experiment is to determine the value of
empirically.
The Buffons needle experiment, in its original form, is to drop a
needle of le
S6880 #13
Variance Reduction Methods
General Techniques
Reduction of simulation cost variance reduction.
General Techniques
1. Importance Sampling
2. Control and antithetic variates
3. Conditioning
4. Use of special features of a problem
A note about hit
S6880 #11
Sampling from Marginal Densities
Possibility of Direct Generation
Problem: Given a random vector X = (X1 , , Xk )t .
Want: to generate a random variate from its i th
component Xi .
If: components are independent or are normal, then
its straightf
S6880 #12
Monte Carlo (Techniques for) Integration
What is Monte Carlo Method
Use a stochastic model as a mean to study a deterministic
system. Example includes Monte Carlo integretation.
Monte Carlo Integration, an Example
1
1 x 2 dx
A deterministic prob
S6880 #11b
Sampling from Marginal Densities, An Example
An Example
Outline
1
An Example
An ExampleBinomialBetaPoisson Model
Hatching Insect Eggs Example in Full Form
(WMU)
S6880 #11b
S6880, Class Notes #11b
2/7
An Example
BinomialBetaPoisson Model
Hat
S6880 #10
Sampling Methods
Sampling with Replacement
Want: Select a sample of size n with replacement from
cfw_x1 , x2 , , xN .
Method: Generate discrete uniform from the indices
cfw_1, 2, , N and index these indices.
Algorithm: Generate U1 , , Un U (0,
S6880 #9
Generating Order Statistics
Direct Generation and Sorting
X F (x ), cost = sampling + sorting
Example sorting algorithm: quick sort, need O (n log n)
comparisons.
Inversion Method
Generate U1 , , Un U (0, 1)
Sort U(1) , , U(n)
Inverse X(1) = F 1
S6880 #8
Generate Nonuniform Random Number #2
Marsaglias Method for Generating Normal r.v.s
rectanglewedgetail
First note that x N (0, 1) can be
generated by generating x from a half
normal and assigning a random sign
to it. That is, need only to gener
S6880 #7
Generate Nonuniform Random Number #1
Inverse CDF
F (X ) U (0, 1) if X is continuous. That is, for continuous r.v. X ,
X = F 1 (U ). In general,
dene F 1 (u ) = mincfw_x : F (x ) u ,
then
X F 1 (U ) for U U (0, 1).
Exponential
X E () where = E (X
S6880 #6
Random Number Generation #2: Testing RNGs
Theoretical Tests
no realizations of the generator needed, decide whether the
period is large enough. Use spectral test. It requires the
assumption that the generator is of full period. The method
compare
S6880 #5
Random Number Generation #1: Generate Uniform
Random Number
General Formula
xi (xi 1 + c ) ( mod m), i = 1, 2, 3,
where xi , , c , m are integers, 0 xi < m. Start out at x0
(random seed).
xi
Then ui =
: U [0, 1)
m
It is called mixedcongruential
S6880 #4
Numerical Computation
MachineRepresentable Numbers
Suppose base is (usually 2) then
di i e , where
r =
i =1
d1 = 0, 0 di 1, i , and m e M (m and M are (nite)
integers). Note: not all r R are considered.
Approximation Equation
Machine representab
Matrix Algebra in R
William Revelle
Northwestern University
January 24, 2007
Prepared as part of a course on Latent Variable Modeling, Winter, 2007
and as a supplement to the Guide to R for psychologists.
email comments to: revelle@northwestern.edu
A Matr
Stat1600
Solution to Midterm TakeHome Exam
Problem #16 Give explicit equations for the p.d.f.s of all components in the Marsaglias normal generator when a = 0.5, r = 4. In addition, specify pi s for these components.
Denote F the c.d.f. of the half norma
1
MATLAB R / R Reference
July 14, 2011
David Hiebeler
Dept. of Mathematics and Statistics
University of Maine
Orono, ME 044695752
http:/www.math.umaine.edu/~hiebeler
I wrote the rst version of this reference during Spring 2007, as I learned R while teach
Introduction
Examples
Packages
A
The Joys of LTEX
A 45 minute lecture, with examples, introducing the worlds
standard typesetting language.
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
June 22, 2009
http:/wwwrohan
RN
Random Numbers
Copyright (C) June 1993, Computational Science Education Project
Remarks
Keywords: Random, pseudorandom, linear congruential, lagged
Fibonacci
1. List of prerequisites:
some exposure to sequences and series, some ability to work in base
Introduction
Examples
Packages
A
The Joys of LTEX
A 45 minute lecture, with examples, introducing the worlds
standard typesetting language.
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
June 18,2013
http:/wwwrohan.
Introduction
Examples
Packages
A
The Joys of LTEX
A 45 minute lecture, with examples, introducing the worlds
standard typesetting language.
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
June 18,2012
http:/wwwrohan.