Econ 221 - Assignment 2 Answer Key
October 3, 2013
1S = fF F; F M; M F; M M g
aA = fF F g
bB = fM M g
cC = fM F; F M; M M g
dA\B =?
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fA\C =?
gA [ C = fF F; M F; F M; M M g = S
hB \ C = fM M g = B
iB [ C = fM F; F M; M M g = C
jC \ B =
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Econ 221 - Assignment 2 Answer Key
October 3, 2013
1S = fF F; F M; M F; M M g
aA = fF F g
bB = fM M g
cC = fM F; F M; M M g
dA\B =?
eA [ B = fF F; M M g
fA\C =?
gA [ C = fF F; M F; F M; M M g = S
hB \ C = fM M g = B
iB [ C = fM F; F M; M M g = C
jC \ B =
Assingment 3 Solutions
March 24, 2014
1
1. (a) (Dichotomized Regression) First consider E[i ]. In order to compute this expectation
x
we need to know the density of xi f (i ). But since xi is binary random variable it
x
takes only two values:
P (i = 1) =
ECON 221 Introduction to Probability and
Statistics I
Midterm II
Solutions
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the second midterm.
November 25, 2013
Common Distributions
CD
Assignment 2 Solutions
April 5, 2014
1
1. Assume p(z) is a random variable. Then Fp (x) = P (p(z) < x). Bu this can be written
as:
P (2(1 (|z|) < x) = P (|z|) > 1
x
2
(1)
= P 1 (|z|) > 1 1
= P |z| > 1 1
x
2
= 1 P |z| 1 1
x
2
(3)
x
2
x
x
z 1 1
2
2
x
Assignment I Solutions
March 9, 2014
1. We have P (A|B) = P (A B)/P (B). But since A B we know that A B = A. Thus P (A B) = P (A)
and nally we get P (A) = P (A)/P (B)
2. Consider the expectation E (Xh(Y )|Y )
This can be wrtitten as E (Xh(Y )|Y ) =
xh(y)f
Assignment 2 Solutions
March 24, 2014
1
1. x E n the norm of
x
x
is given by
1 2
x
x
x
x
x=
2
2
= 1.
Consider two vectors x, y E n . Now we will nd norm of sum of normalized x and y:
y
x
+
x
y
x
y
+
x
y
xx
yy
2x y
+
+
2
x
x y
y 2
xy
= 2 1+
x y
=
(1)
(2)
L
Econ 221 - Assignment 3 Answer Key
March 16, 2014
1)
Ri =the plane is in region i where i=1,2,3
P (Ri ) = 1=3
U=search of region 1 was unsuccessful
P (U nR1 ) = 1
i
a)
P (R1 U )
=
=
P (U R1 ):P (R1 )
P (U R1 ):P (R1 ) + P (U R2 ):P (R2 ) + P (U R3 )P (R3
ECON 221 HOM EW ORK 5 SU GGEST ED SOLU T ION S
1) a)T here are 9 possible assignments of construction jobs to the 3 f irms :
32 = AA; AB; AC; BA; BB; BC; CA; CB; CC and these assignments are equally likely
meaning that the probability of each of them is 1
Econ 221 - Assignment I Answer Key
September 26, 2013
1- a-The population of interest is the total number of adult residents in the
state. Since the state includes too many adult residents, we should go about
random sampling in which we choose a sample re
ECON 221 Introduction to Probability and
Statistics I
Midterm I
Solutions
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the rst midterm.
October 9, 2013
1. [10 points] A random sampl
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Econ 221 - Assignment I Answer Key
September 26, 2013
1- a-The population of interest is the total number of adult residents in the
state. Since the state includes too many adult residents, we should go about
random sampling in which we choose a sample re
Econ 221 - Assignment 3 Answer Key
March 16, 2014
1)
Ri =the plane is in region i where i=1,2,3
P (Ri ) = 1=3
U=search of region 1 was unsuccessful
P (U nR1 ) = 1
i
a)
P (R1 U )
=
=
P (U R1 ):P (R1 )
P (U R1 ):P (R1 ) + P (U R2 ):P (R2 ) + P (U R3 )P (R3
ECON 221 Introduction to Statistics
Chapter 41
Continuous Random Variables
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Table of Contents
1 Introduction
2
2 The Probability Distribution for a Continuous R
ECON 221 Introduction to Probability and
Statistics I
Midterm I
Solutions
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the rst midterm.
October 9, 2013
1. [10 points] A random sampl
ECON 221 Introduction to Probability and
Statistics I
Midterm
Fall 2013
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Instructions
You have 180 minutes. Answer every question. Allocate your time as suggest
ECON 221 Introduction to Statistics
Chapter 31
Discrete Random Variables
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Table of Contents
1 Introduction
2
2 The Probability Distribution of a Discrete Random
ECON 221 Introduction to Probability and
Statistics I
Midterm II
Solutions
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the second midterm.
November 25, 2013
Common Distributions
CD
ECON 221 HOM EW ORK 5 SU GGEST ED SOLU T ION S
1) a)T here are 9 possible assignments of construction jobs to the 3 f irms :
32 = AA; AB; AC; BA; BB; BC; CA; CB; CC and these assignments are equally likely
meaning that the probability of each of them is 1
ECON 221 Introduction to Probability and
Statistics I
Midterm I
Mirza Troki
c
trokic@bilkent.edu.tr
Department of Economics, Bilkent University, Ankara, Turkey
Instructions
You have 80 minutes. Answer every question. Allocate your time as suggested by the