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.
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
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
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
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
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
[email protected]
Offi
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.
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
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, [email protected]
Michael Hornstein, [email protected]
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
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
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
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
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
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
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
LAB TICKET, Part 1
Pointer 5. Which is the regression model you would pick for Calcium? Redraw the scatterplot and add
the fitted line. Note the code for this.
We would pick the 3rd regression model for Calcium, since looking at the residuals for the regr
Stats 408
Exam 1 Review
System
System- a collection of components that come together repeatedly to achieve a purpose
Purpose- an assertion that leads to a win for everyone if achieved (maximizing profit cant be,
because it usually isnt a win for everyone)
Stats 408 Exam 1 Review
System:
A system is a collection of components that come together repeatedly to achieve a
purpose
The purpose of The Goal: to maximize profits cannot be the purpose of a system
because it does not satisfy a win for everyone, ever
Stats 408
Lecture 2
First Step: once our purpose is established, we begin the journey by creating a
model of our purpose. There are many models, but one commonly used is a
measurement that reflects the purpose.
Measurement
- the way we make the purpose ex
Stats 408 exam review
Chapter 1:
System: A collection of components that come together repeatedly for a purpose
Purpose: A win for everyone in the system. Maximizing profit is not a purpose, despite what
The Goal may tell us. It is not a purpose because m