STATE OF RHODE ISLAND AND PROVIDENCE PLANTATIONS
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Solution to HW 4
Question 2.1 (i) Show that the expectation of complex valued random
variables is linear, i.e.,
E(aX + bY ) = aE(X) + bE(Y ) ,
where a, b C and X and Y are integrable.
(ii) Show that
Cov(X, Y ) = E(X Y ) E(X)E(Y ) ,
for square integrable X
The converse, however, is not always true.
Cov(X, Y ) can be 0 for variables that are not independent.
For an example where the covariance is 0 but
X and Y arent independent, let there be three
outcomes, (1, 1), (0, 2), and (1, 1), all with the
Example Sheet 1 - Solutions
Comments and corrections should be emailed to [email protected]
1. Let cfw_Xt be a weakly stationary process with mean zero and let a and b be constants.
(a) If Yt = a + bt + st + Xt
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R Installation and Administration
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R Core Team
This manual is for R, version 3.3.1 (2016-06-21).
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NANYANG TECHNOLOGICAL UNIVERSITY
SEMESTER II EXAMINATION 2010-2011
MAS 451 Time Series Analysis
TIME ALLOWED: 2 HOURS
INSTRUCTIONS TO CANDIDATES
1. This examination paper contains FOUR (4) questions and comprises
FIVE (5) printed pages including
Rhode Island DMV Document Checklist
LICENSE & ID CARDS
A certified birth certificate (not a
copy) or Proof of Identity Document
Not a Face Card
Not a Heart
P(Not a Face Card)=P(C)=
P(Spade, Club, or Diamond)=P(D)=
P(C and D)=
P(C or D)=
Shuffle a deck of playing cards a
Chapter 6 ProbabilityTree Diagrams and the General Multiplication Rule
According to Forrest Gump, Life is like a box of chocolates. You never know what youre gonna get.
Suppose a candy maker offers a special Gump Box wi
Chapter 8 Review
Statistical inference draws conclusions about a population on the basis of sample data and uses probability to indicate
how reliable the conclusions are. A confidence interval estimates an unknown parameter.
The probabilities in confidenc
Chapter 6 Review
A random variable summarizes the outcomes of a chance process with a single number. Its probability distribution
specifies the values that the random variable can take and how often it takes those values. We can use the probability
Homework Section 7.1
1. Identify the population, the parameter, the sample, and the statistic in each setting.
a. A random sample of 1000 people who signed a card saying they intended to quit
smoking were contacted 9 months later. It turned out that 210 (
2008 AP Statistics Exam Debriefing
Most students answer in context
Most students know that a comparison should address center, spread, and shape
Most students recognize that a boxplot is a graph of the five-number summary
Ch 6-8 Review
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
Foresters use regression to predict the volume of timber in a tree using easily measured quantities such as diameter. Let y be
the volume o
Homework Section 4.1
1. A high schools student newspaper plans to survey local businesses about the importance of
students as customers. From an alphabetical list of all local businesses, the newspaper staff
chooses 150 businesses at random. Of these, 73
1. In June 2008, 88% of automobile drivers filled their vehicles
with regular gasoline, 2% purchased midgrade gas, and 10%
bought premium gas. Of those who bought regular gas,
28% paid with a credit card. Of customers who b
Homework Section 4.3
1. Do abandoned children placed in foster homes do better than similar children placed in an
institution? The Bucharest Early Intervention Project found that the answer is a clear Yes.
The subjects were 136 children abandoned at birth
5.1 Day 2 Simulations
Simulation the imitation of chance behavior, based on a model that accurately reflects the situation.
4 step process for performing a simulation
STATE: What is the question of interest about some chance process?
PLAN: Describe how to
Homework Section 6.3
1. Which of the following scenarios describe binomial settings? If the scenario is not a binomial
setting, discuss why not.
a. Seed Depot advertises that its new flower seeds have an 85% chance of germinating.
Suppose that the company
AP Statistics Chapter 10 Notes: Estimating with Confidence
10.1 Confidence Interval Basics
Confidence Interval A level C confidence interval is of the form estimate margin of error
The confidence level C gives us the probability that the interval will cap
AP Statistics Test Chapters 7-9
1. A recent study claims that for every 5 days absent, a students grade point average suffers 2%. What is the
slope of the regression line implied by this statement?
2. Find the slo
AP STATISTICS: AGAINST ALL ODDS
Video 1 Worksheet
WHAT IS STATISTICS?
What is the narrators job? _
How were the two groups of children different in the creativity experiment?
Tell one way that Dominos used statistics. _
What are the t
2 September 2014
Mr. James OConners
Special Assignment #1
Some people says that minute seems like a long time (like when holding your
breathe under water.) Others say, Time flies. How well can people determine a
AP Statistics Chapter 1 Free Response Practice Test
1. The test grades for a certain class were entered into a Minitab worksheet, and then
Descriptive Statistics were requested. The results were
AP Statistics Chapter 9 Notes: Sampling Distributions
9.1 Sampling Distributions
Parameter a number that describes a population (usually unknown)
Statistics a number that describes a sample (used to estimate a parameter)
Chapter 1: Exploring Data
AP Statistics Preliminaries
Statistics is the science (and art) of learning from data.
Individuals are the objects described by a set of data. Individuals may be people, but they may also be
animals or things.
A variable is any c
Name: _ Block: _ Date: _
1. To pick out the five number summary from descriptive statistics provided by Minitab.
2. To identify mean and standard deviation for a data set.
3. To compare t
An Example of Sampling Distributions: Ratio Estimation (Using SRS)
Reconsider the population (N=6):
The population mean is
and its standard deviation is = 64/ 6 3.27 .
For simple-random samples (SRS) of size n = 2, we again have the foll