Instructions for the Gibbs Sampling Problem and R Commands
(* may be completed with a partner *)
The goal of this problem is to do a Bayesian analysis of the distribution of normal body
temperature readings for healthy male and female individuals. The dat
Homework #3
Timothy Reese
02/06/12
66) Let the unknown probability that a basketball player makes a shot successfully be . Suppose your prior on is uniform on [0, 1] and that she
then makes two shots in a row. Assume that the outcomes of the two
shots are
Homework #2
Timothy Reese
02/01/12
62) Show that the gamma distribution is a conjugate prior for the exponential
distribution.
Proof. Likelyhood function: fX | (x|) =
Prior Gamma: f () = () 1 e
n
i=1
exi = n e
n
i=1
xi
n
Posterior: f|X (|x) n e i=1 xi 1 e
Homework #1
Timothy Reese
01/30/12
5) Suppose that X is a discrete random variable with P (X = 1) = and
P (X = 2) = 1 . Three independent observations of X are made:
x1 = 1, x2 = 2, x3 = 2.
d) If has a prior distribution that is uniform on [0, 1], what is
Timothy Reese
05/02/12
One-Way ANOVA Homework
1. One of the symptoms of depression is a lack of enthusiasm for an activity that would
normally be enjoyable. A medication was developed that was designed to address this
problem. Fifteen volunteers were rand
Timothy Reese
Math 440B
03/07/12
Chapter 13.
5)
: Ethnic origin and attitudes toward roles of woman are independent. i.e
: They are not independent.
Chi-Square Test: C2, C3
Ethnic Origin
Yes
No
Expected counts are printed below observed counts
Chi-Square
BOOTSTRAPPING HOMEWORK
Not surprisingly, the pulse rates of skydivers increase dramatically at the
beginning of a jump. Here are the electronically monitored maximum heart rates of ten
Navy parachutists as they exited a plane flying at 10,000 feet:
160
18
Timothy Reese
Math 440B
02/12/2012
Bootstrap Heart Rates
Confidence Interval for
Confidence Interval for
5th smallest of :-5.2
6th smallest of :-4.9
Midpoint:
5th largest of : 5.2
6th largest of : 5.1
Midpoint:
This gives the 95% confidence interval for :
Timothy Reese
Math 440B
05/04/12
ANOVA
26)
Two-way ANOVA: Concen versus Drug, Dog
Analysis of Variance for Concen
Source
DF
SS
MS
Drug
2
1.081
0.540
Dog
9
0.517
0.057
Error
18
2.208
0.123
Total
29
3.806
Drug
1
2
3
Mean
0.43
0.47
0.85
Dog
1
2
3
4
5
6
7
8
9
Problem #36
Regression Analysis: Deflection versus Load
The regression equation is
pressure = 26068 - 39.9 temperature
Predictor
Constant
temperature
Coef
26068.0
-39.8736
S = 25.3068
SE Coef
16.2
0.5042
R-Sq = 99.7%
T
1612.23
-79.08
P
0.000
0.000
R-Sq(ad
Phillip Oh
Math494
Professor Shapiro
What is Operations Research?
Operations research (also referred to as OR- is used to find a better way to solve problems such
as:
A problem that as the complexity and specialization of an organization increases, OR is
Phillip Oh
Math494
Professor Shapiro
Queuing Theory
Queues waiting lines.
Queuing Theory The study of waiting in all of its various guises.
Queuing theory uses queuing models to represent the various types of queuing systems that arise
in practice.
The Ba
Phillip Oh
Math494
Professor Shapiro
Density Flow Relationship
Introduction
For decades, Los Angeles has been plagued with freeway traffic. Is there a way to fix
this? I came up with a mathematical model that shows the relationship between density and flo
Phillip Oh
Math494
Professor Shapiro
First Mathematical Model
*Picture from http:/nexus.umn.edu/theses/shantanudas_thesis.pdf*
Qfin + Qiron = Qfout + Qirout
The above equation makes sense because the cars on the freeway must come out of the freeway.
But t
Phillip Oh
Math494
Professor Shapiro
First Idea & Stochastic Model
The following was an initial idea that I could not follow through on.
Focusing on a 10 mile stretch of freeway. Dividing the 10 mile stretch into sections of 1/10
mile. 100 separate sectio
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 17 Personal Reflection Essay
This chapter is entitled Dividends, Stock Repurchases, and Payout Policy. It writes about
the different types of dividends, the payment process for dividends, stock repurchase, pros and
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 17 Corporate Finance Article
The Price of Gold Is Crashing. Heres Why
Businessweek.com
Edited by Brahm Canzer
http:/www.businessweek.com/articles/2013-04-15/the-price-of-gold-is-crashing-dot-hereswhy#r=most popular
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 16 Personal Reflection Essay
This chapter is entitled Capital Structure Policy. It writes about the two Modigliani and
Miller propositions and their relevance to capital structure decisions, the pros and cons of deb
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 16 Corporate Finance Article
Bet against Chipotle? Bad move
CNNMoney.com
Edited by Brahm Canzer
http:/money.cnn.com/video/investing/2013/04/19/investing-the-buzz-chipotle.cnnmoney/
Questions for Discussions:
Summar
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 15 Personal Reflection Essay
Chapter 15 is entitled How Firms Raise Capital. It writes about bootstrapping, the role of
venture capitalists, the pros and cons of going public, why investment bankers prefer new
secur
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 15 Corporate Finance Article
American Girl drives Mattel sales
CNNMoney.com
Edited by Brahm Canzer
http:/money.cnn.com/video/investing/2013/04/17/investing-the-buzz-mattel.cnnmoney/
Questions for Discussions:
What
Phillip Oh
Fin303L
Prof. Yanbo
Chapter 14 Personal Reflection Essay
Chapter 14 is entitled Working Capital Management. This chapter writes about the
computations and importance of working capital, the operation and the cash conversion cycles,
the pros and
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 14 Corporate Finance Article
When to hold or fold your stock
CNNMoney.com
Edited by Brahm Canzer
http:/money.cnn.com/video/pf/2013/04/09/pf-when-to-sell-stocks-romans.cnnmoney/
Questions for Discussions:
Summarize
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 13 Personal Reflection Essay
Chapter 13 is entitled The Cost of Capital. This chapter writes about the weighted
average cost of capital and why it is often used as a discount rate for evaluation, calculating the
cos
Phillip Oh
Fin303OL
Prof. Yanbo
Chapter 13 Corporate Finance Article
Microsoft and other PC stocks crash
CNNMoney.com
04/15/13
Edited by Brahm Canzer
http:/money.cnn.com/video/investing/2013/04/11/investing-the-buzz-pc-dead.cnnmoney/
Questions for Discuss