ECON 221 Introduction to Probability and
Statistics I
Midterm II
Solutions
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the se
1
Optimization
1.1
Introduction to maximization and minimization
Definition 1 (Maximizer, minimizer). Let S Rn and f a real valued
function on S, i.e., f : S R. A point x S is said to be a (global)
ma
Boundary points, open, closed, bounded and compact sets, interior points
The distance between any two points x = (x1 , x2 , . . . , xn ) and y = (y1 , y2 , . . . , yn )
in Rn , denoted d (x, y), is de
ECON 225:
Mathematics for Economists
Homework I
Due: September 27, 2017
1) Let v = (2, 1) and w = (1, 3). For the questions below draw a well labeled
graph and label all the vectors asked clearly.
a.
Box and Whisker Plot is a graph that describes the shape of the distribution in terms of the five-number summary: the
minimum value, first quartile, median, third quartile, and the maximum value. The
CLASS EXAMPLES
CHP 4 Discrete Random Variables & Probability Distributions
Ex 1 :
Consider the following probability distribution function (pdf). Let X denotes number of cars
sold in a day.
X
0
1
2
3
CLASS EXAMPLES
CHP 7 & 8 Estimation
Ex 1 :
A polling company is under contract with an advertising agency to update estimates as to the
mean number of hours spent by mid-westerners watching television
CLASS EXAMPLES
CHP 2 Describing Data: Numerical
Ex 1 :
A random sample of 5 business economists was asked to predict the percentage growth in the
consumer price index (CPI) over the next year. The for
EXAMPLE 1
Organizing & Summarizing your data
An occupational analyst obtained the time (in seconds) for a random sample of n=100 support
staff to complete a particular task. The goal is to complete th
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 \
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 r
ECON 221 Introduction to Probability and
Statistics I
Midterm I
Solutions
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the rst
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
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 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 )
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
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
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| >
ECON 221 Introduction to Probability and
Statistics I
Midterm II
Solutions
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the se
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ECON 221 Introduction to Probability and
Statistics I
Midterm
Fall 2013
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Instructions
You have 180 minute
ECON 221 Introduction to Probability and
Statistics I
Midterm I
Solutions
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Suggested solutions to the rst
ECON 221 Introduction to Statistics
Chapter 41
Continuous Random Variables
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Table of Contents
1 Introduct
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 )
ECON 221 Introduction to Statistics
Chapter 1
Mirza Troki
c
[email protected]
Department of Economics, Bilkent University, Ankara, Turkey
Table of Contents
1 Introduction
2
2 Descriptive Statistic
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