Problem Set #3
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 3, 2009
Question One
1. Write down the definition of a cumulative distribution function (CDF). Explain what
it means in words, perhaps using an
Problem Set #3
14.30  Intro. t o Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 3, 2009
Question One
1. Write down the definition of a cumulative distribution function (CDF). Explain
what it means in words, perhaps using a
(1) Why is the mean an inappropriate measure of central tendency in a very skewed
distribution?
( X
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(2) a. What does
i
)
X mean?
i=1
b. What value does the above always equal?
(3) A researcher collected several sets of data. For each indicate which mea
3A
300
28
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VIATH
Solutions Manual to Walter
Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont Chapter 1
The Real and Complex
Number Systems
Exercise 1.1 If 7" is rational (7' 7E 0) and :2: is irrational, prove that
2A
300
28
1976
Supp.
VIATH
Solutions Manualto Walter
* Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont Chapter 2
Basic TopolOgy
Exercise 2.1 Prove that the empty set is a subset of every set.
Solution. Let Z denote the empt
DA
300
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WATH
Solutions rManual to Walter
‘ Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont Chapter 3
Numerical Sequences and
Series
Exercise 3.1 Prove that convergence of {57,} implies convergence of Is
the con
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300
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Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont Chapter 7
Sequences and Series of
Functions
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300
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Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont Chapter 4
Continuity ‘
Exercise 4.1 Suppose f is a real function deﬁned on R1 which satisﬁes
,gim mm + h) — f<m — h>1= 0
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Mathematical Analysis
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Chapter 6 V'
The Riemann—Stieltjes
Integral,
Exercise 6.1 Suppose oz increases on [(1, b], a g
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Rudin’s Principles 0f
Mathematical Analysis
Roger Cooke, University of Vermont 5333;,
Chapter 11
The Lebesgue Theory
Exercise 11.1 If f 2 0 and LE f dp = 0, prove that f (IE) 2 0 almost every
where o
Problem Set #6
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, April 7, 2009
Question One
Let X be a random variable that is uniformly distributed on [ O , 1 ] (i.e. f (x) = 1 on that
interval and zero elsewhere)
Problem Set #4
14.30  Intro. t o Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 17, 2009
Question One
Suppose that the P D F of X is as follows:
e"
0
f (4=
forx > 0
forx5O
1. Determine the P D F for Y = Xi .
2. Determine
Problem Set #2
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, February 24, 2009
Question 1
Recall that a random variable X has the binomial distribution if
where n is the number of trials and p is the chance of
Problem Set #2

Solutions
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, February 24, 2009
Question 1
Recall that a random variable X has the binomial distribution if
where n is the number of trials and p is th
Problem Set #l

Solutions
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, February 17, 2009
Instructions
You may work together to solve the problems but must each hand in independentlywritten solutions,
so make
Problem Set #5

Solutions
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 31, 2009
Question One
The convolution formula is a useful trick when we are interested in the sum or average of
independent random
Problem Set #4

Solutions
14.30  Intro. t o Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 17, 2009
Question One
Suppose that the P D F of X is as follows:
e"
0
f (4=
1. Determine the P D F for Y
=X
forx > 0
forx50
i.
So
Problem Set #7
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, April 14, 2009
Question One
We just learned about the standard Normal distribution with PDF 4(x) and CDF @(x).
Let's familiarize ourselves with it, a
Problem Set #7
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, April 14, 2009
Question One
We just learned about the standard Normal distribution with PDF 4(z) and CDF @(z).
Let's familiarize ourselves with it, a
Problem Set #6

Solution
14.30  Intro. t o Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, April 7, 2009
Question One
Let X be a random variable that is uniformly distributed on [ O , 1 ] (i.e. f (x) = 1 on that
interval and zer
Problem Set #5
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, March 31, 2009
Question One
The convolution formula is a useful trick when we are interested in the sum or average
of independent random variables. I
(1) Why is the mean an inappropriate measure of central tendency in a very skewed
distribution?
(2) a. What does (XX) mean?
b. What value does the above always equal?
(3) A researcher collected several sets of data. For each indicate which mean of centra
9.07 Practice Final (fall 2004):
1. Health and Nutrition Examination Survey of 19761980 recorded handedness of
the 2,237 surveyed Americans aged 2534:
At 1% significance level can you conclude that gender and handedness are not
independent?
Male
Female