January 15, 2008
Homework 1 Solutions
Stat 408
Problem 1. What is a system? Provide an example. Solution. A system is a collection of components that come together repeatedly for a purpose. One example is a school district. It contains administrat
Expected Value
A random variable X has a range of possible values
and probabilities for attaining those values
Example: X = result of a dice roll
X can equal 1,2,3,4,5,6, and P(X=1)=.=P(X=6)=1/6
Expected Value
The reasoning is this: if X can equal 1, 2, 3
STAT 408
GSI: Zhiyuan (Julian) Lu, jlnlu@umich.edu
Michael Hornstein, mdhorn@umich.edu
10% of your grade will be determined by lab attendance and
homework. This 10% will be distributed evenly between
homework and attendance.
Homework will be due each week
Review of Matching Problem
Special case: What is the probability that among N people, at
least one pair has the same birthday? (M = 365)
Let E denote the event that at least one pair has the same
birthday. The probability of not E is
1
364 363
365 (N
.
High efficiency not equal to high effectiveness
Optimizing aspects not equal to moving towards the purpose
Every one doing their best not equal to optimizing system
Time is an element of every system
Measurement
Whats
1. Response
2. Predictors
3. Find the
Homework Set 08
Xintong Zhu
1. Provide a situation where rule 2 of the funnel experiment provides a model.
Rule2ofthefunnelexperimentistochangethepositionofthefunnelbasedonthe
lastlocation.This is a model because it is trying to make the
purpose (landing
Stats 500 HW 3
Due November 5
1. Suppose that a box contains N tickets, and each ticket has a number written on it, which we denote
ti . Suppose we draw n N tickets at random without replacement, and let X1 , ., Xn denote the
numbers we observe on the tic
Statistics 408
Fall 2015
Lecture Week 07
Measures of Variation
Range
Mean Absolute Deviation
Variance standard deviation
Entropy
Range
Range= largest value minus the smallest value
Simple to compute
Ex 1, 3, 7 has a range of 7-1 or 6
However, when we want
Homework 6
Stat 408
Fall 2014
Review Questions
1. Explain why the purpose of a company cannot be either of the following:
i. Maximize Profits
Maximizing profits will create winners and losers in the system. If a company
aims at maximizing the profit, they
Statistics 408
Lecture Week 08 Fall 2015
Sources of Variation
1. Operational Definitions
2: Complexity
3: Aggregation
4: Tampering or Over-control of a Stable
System
Operational Definitions
Two values can differ because we use different
methods of measur
Statistics 408
Fall 2015
Lecture Week 09
Bias
Selection Bias
Respondent Bias
Scientist Bias
Interpretation/ Intervention Bias
Selection Biases
1. Target of the study and the context or set we
study may Differ
Enumerative v Analytic Investigations
Enume
Lab 2: Probability
9/24/2015
Review of Probability
Let E be an event, P(E) its probability
P(E) is between 0 and 1
P(not E)=1-P(E)
Let E and F be two independent events.
P(E and F)=P(E) x P(F)
Review of Probability
E and F are any two events:
P(E|F) i
Prospective vs Retrospective
A Prospective study watches for outcomes, usually
taking a sample and watching it over time (analyzes
P(occurance|factor)
Example: taking a group of people, record weight,
BMI, smoking status, then watching for heart disease.
Problem Solving: A System
Approach
E Rothman
Fall 2015
Statistics 408
0. Outline of Course
Grading Process and Expectations
Models
Problem Solving: A System Approach
1. September, 2015
2. Statistics 408
3. E Rothman
275 West Hall
erothman@umich.edu
Offi
STATISTICS 408 HOMEWORK #3: SOLUTION Problem 1. The physician claims that the probability that a patient has a viral infection is 95%. What does this statement mean (provide an operational definition for this measure)? Is this a property of the indiv
Homework 4 Stat 408 Winter 2008 1. Present a theory as a countermeasure to "The enemy is out there." Solution. A theory to countermeasure "The enemy is out there" would be "The enemy might be in here". Instead of complaining about the things you may
STATS 408 HOMEWORK #5 SOLUTION 1. When would we not want to use range as a measure of variation? We would not want to use range as a measure of variation to compare sets of items that differ in the number of items. As the number of items in a dataset
Homework 6 Stat 408 Winter 2008 1. Describe the regression effect. Solution. The regression effect is that an observation on a feature at one point in time-e.g. your test I score-may be a distance-e.g. so many standard deviations from average-is expe
Statistics 408 Homework Set 7: SOLUTIONS 2008
1. What is knowledge? What is profound knowledge? When would someone with a useful theory not have knowledge? Describe the process of acquiring knowledge? Identify potential bottlenecks in this process.
1. Suppose we find that among couples that have lived together before they marry 60% end in divorce. Further, among couples that did not live together before they marry 45% end in divorce. Identify a variable that subdivides the population into subse
Problem Solving: A System
Approach
Week 04
Fall 2015
Matching Paradoxes
Choose a number between 1 and M
(M=10,000, say). If the numbers are chosen
independently, then we ask each person what
their number is. At what point N is the p or
Probability of at
Statistics 408
Week 03
Fall 2015
How we measure?
Principle: There is no true value of any measure.
When we change the method of measurement, we may change the
value.
Example: What is the population of Ann Arbor?
Including students etc. would change th
Statistics 408
Week 02
Fall 2015
Last Weeks Principles
1. Everyone doing their best my not be best
-Interdependence
-Series System
2. High efficiency of every component may
not be effective
3. Optimization of a model may not help us
improve the world the
Statistics 408
Fall 2015
Week 05
Learning
Two elements are useful theory and action
based on the useful theory
A learning disability-must either keep us from
acquiring useful theory or keep us from acting
on the theory.
When you want to show that you h
HomeworkSet7
Statistics408
Winter2015
1. Describe how the range, mean absolute deviation, the varianceandtheentropymeasures
arecalculatedasmeasuresofvariation.
Therangeofacollecteddatasetcfw_x n
,x
isthevaluemaxcfw_x n
,x
mincfw_x n
,x
.
1
1
1
Suppose we