Exam 1
14 30 Fall 2004
Herman Bennett
Instructions: This exam is closed-book and closed-notes. You may use a simple calculator.
Please read through the exam in order to ask clarifying questions and to
Chapter 11: Interval Estimation
Section 5: The Estimation of differences between Proportions
1 1 1
var
1
n1
2 1 2
var
2
n2
Assuming that we have independent random samples from two binomial
Chapter 11: Interval Estimation
Section 1: Introduction
As we said at the beginning of Chapter 10, there are two types of
estimation of parameters that we will look at.
1. Point Estimation
2. Interval
Chapter 11: Interval Estimation
Section 6: The Estimation of Variances
In this section, we will look at estimating variances and standard deviations.
Recall: For a random sample taken from a normal po
Chapter 11: Interval Estimation
Section 7: The Estimation of the Ratio of Two Variances
2
2
Recall: For S1 and S 2 , variances of independent random samples of size n1 and n2
taken from normal populat
MK 4900 Course Information Document
Fall Semester 2015
MK 4900, Marketing Strategy (nee Marketing Problems), is the capstone course
in the Marketing major. The role of the course is to hone your marke
Marketing 4600: International Marketing
GROUP PROJECT ASSIGNMENT TO BE COMPLETED IN LIEU OF CLASS ON 09/03/2015
Note: There will be no class on 09/03/15
1. Read the entire Country Note Book Guidelines
REVISED
GEORGIA STATE UNIVERSITY
J. MACK ROBINSON COLLEGE OF BUSINESS
PROFESSIONAL SALES, CRN 86978, MK 4330-005
FALL SEMESTER 2015
MONDAYS AND WEDNESDAYS, 12:00 1:15
CLASSROOM SOUTH, ROOM 207
INSTRUC
14.30 PROBLEM SET 1 - SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
For any A and B, we can create two sets that are disjoint and
exhaustive on B: A \ B and AC \ B. Thus
!
"
Pr (B) = Pr (A \ B
Formula Sheet Exam 2
MIT 14 30 Spring 2006
Herman Bennett
Var X) = 2 = E[ X
)2 ]
Cov X, Y ) = E[ X
X, Y ) =
X)
= E X).
Y
Y )]
Cov X, Y )
X Y
P |X
fY y1 , y2 , ., ym ) =
E X)
.
t
E X)| t)
4)
5)
V ar
14.30 PROBLEM SET 5
TA: Tonja Bowen Bishop
Due: Tuesday, April 4, by 4:30 p.m.
Note: The rst three problems are required, and the remaining two are
practice problems. If you choose to do the practice
14.30 PROBLEM SET 4
TA: Tonja Bowen Bishop
Due: Tuesday, March 21, by 4:30 p.m.
Note: The rst three problems are required, and the remaining two are
practice problems. If you choose to do the practice
14.30 Exam #1 Solutions
Thursday, October 7, 2004
Guy Michaels
Question 1:
A. True/False/Uncertain:
i. False. Two events can be neither disjoint nor exhaustive. For example, consider the
outcome of a
Exam 2
MIT 14 30 Spring 2006
Herman Bennett
Instructions: This exam is closed-book and closed-notes. You may use a simple calculator.
Please read through the exam in order to ask clarifying questions
14.30 PROBLEM SET 2
TA: Tonja Bowen Bishop
Due: Tuesday, February 28, 2006 , by 4:30 p.m.
Note: The rst four problems are required, and the remaining two are
practice problems. If you choose to do the
14.30 EXAM 2 - SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Question 1
A.
(i)
F alse. The result E (g (X) = g (E (X) only holds for linear
functions of X, because integration is only distributive over lin
Chapter 13: Tests of Hypothesis involving means, variances, and
Proportions
Section 1: Introduction
Definition 13.1. Test of Significance: A statistical test which specifies a simple
null hypothesis,
Chapter 13: Tests of Hypothesis involving means, variances, and
Proportions
Section 2: Tests Concerning Means
A researcher thinks that students who arrive less than 10 minutes
before an standardized e
Chapter 8: Sampling Distributions
Section 5: The t Distribution
Previously, we have discussed that the set of possible samples of size n
from a normal population with mean and standard deviation is no
Chapter 8: Sampling Distributions
Section 6: The F Distribution
The F distribution more theoretically as shown in Theorem 8.14 is a
sampling distribution of two random chi-square variables.
Go to Theo
Chapter 11: Interval Estimation
Section 2: Estimation of Means
Recall:
A sample mean X is an unbiased estimator of the mean of a normal
population.
x
2
x
2
n
P Z z / 2 1
X
P
z / 2 1
n
X
P
z
Chapter 8: Sampling Distributions
Section 3:
The Distribution of Mean: Finite Populations
Consider the experiment of selecting one or more values from a finite set of
numbers cfw_c1, c2, . . . , cN. N
Chapter 12: Hypothesis Testing
Section 1: Introduction
Point Estimate A single value found from taking a sample. It is used to estimate
a parameter of a population. For a population of continuous meas
Chapter 8: Sampling Distributions
Section 2: The Distribution of Mean
Previously we have looked at distributions of a random variable X for some
linear combination of X.
Sample means from samples of a
Chapter 11: Interval Estimation
Section 4: The Estimation of Proportions
The binomial distribution can be approximated by the normal distribution when n
is large.
Z
X n
n (1 )
As we have seen earlier,
Chapter 11: Interval Estimation
Section 3: The Estimation of Differences Between Means
X
Z=
1
X 2 1 2
12
n1
22
n2
P z / 2 Z z / 2 1
Doing the substitution for Z, we can get
12 22
12 22
P x1 x2
Chapter 8: Sampling Distributions
Section 4:
The Chi-Square Distribution
In this section we will look at the chi-square distribution. The value of a chisquare random variable is 2. is the lower case G
Chapter 12: Hypothesis Testing
Section 5: Power of a Test
The previous sections covered present simple hypotheses of the form:
H0: = 0
H1: = 1
Given , the probability of making a type I error, we coul
Chapter 12: Hypothesis Testing
Section 6: Likelihood Ratio Tests
In Section 12.4, we learned how to use the Neyman-Pearson lemma to construct
most powerful critical regions given a simple null hypothe
Chapter 13: Tests of Hypothesis involving means, variances, and
Proportions
Section 3: Tests Concerning Differences Between Means
It is common to want to compare the differences between population
mea
MATHEMATICAL STATISTICS I
October 29, 2015
()
MATHEMATICAL STATISTICS I
October 29, 2015
1/3
Outline
Review
moment-generating function
product moment
covariance
conditional mean and variance
()
MATHEM
t8
Socfw_uLi on
HW
i
rcfw_) Yes
(,c)
No,
kturc fo + frrt fl r fivi /
gemue fixteo
ucfw_
tf,"*
t
ry cfw_c,+ fr.t r fenfw*f,g=l , utoAa,e ,=i
ttl gy fort'. + f v) =l , u,u.lane. c=h
t.t 4etuLls o *'k4 -