C HAPTER
1
What Is Statistics?
1.1 Introduction
1.2 Characterizing a Set of Measurements: Graphical Methods
1.3 Characterizing a Set of Measurements: Numerical Methods
1.4 How Inferences Are Made
1.5
PROBLEM SET 2
1) Suppose that X is a random variable that has the probability function
0.3 = 8
P X = k = p k = 0.2 = 10
0.5 = 6
a) What is the expected value of X?
b)
ECON 205 PS 4
1) For two continuous variables and with probability densitiy functions f1 and f2
respectively, the random variable Y with probability density function
ECON 205 Problem Set 3
1) Let Y be a discrete random variable with mean and variance 2. If
a and b are constants, prove that;
a) E(aY+b)=aE(Y)+b=a+b
b) Var(aY+b)=a2V
ECON 205 PS 4
1) For two continuous variables and with probability densitiy functions f1 and f2
respectively, the random variable Y with probability density function
ECON 205 PS4 Solutions
1.
b)
2.
3.
4.
5.
6. Let Y be the daily water demand in city X in the early afternoon. Then, Y is exponential
with = 100 cfs.
7. We want to find the capacity a so that ( ) = 0.0
ECON 205 Problem Set 5
4. Let Y1 and Y2 have the joint probability density function given by
6 1 ! , 0 ! ! 1
! , ! =
0,
a) Show that this is a probabili
ECON 205 HW1 Solutions
1.
There is 36 possible outcome.
11 of the 36 outcomes gives Z=1
If X=1 and Y=1, then Z=1
If X=1, and Y=2,3,4,5,6 then Z=1
If Y=
PROBLEM SET 2
1) Suppose that X is a random variable that has the probability function
0.3 = 8
P X = k = p k = 0.2 = 10
0.5 = 6
a) What is the expected value of X?
b
ECON 205 PROBLEM SET 7
1) The pdf of X is given as
6 1 0 < < 1
() =
0
a) Find the pdf of the random variable Y which is defined as = 2 + 1
b) Find the probability density of Y=X3
2) Let X and Y b
ECON 205 HW 1
Due Date: March 27th 2015, 17:00 (CHAPTERS 2&3)
1) Two balanced dice are rolled, one is green and one is red. Let X be the
value facing up on the green die and Y be the value fac
ECON 205 HW 3 (Due to May 25th)
1)
Suppose X is distributed uniformly on the interval [0,1]. A random
variable defined as U=3X+1. Find the probability density functio
PS5 (Chapter 4 Z table and Chapter 5.1,5.2)
1) The length of human pregnancies from conception to birth approximates a normal distribution with a
mean of 266 days and a standard deviation of 16 days.
Middle East Technical University
Department of Economics
Spring 2013-2014
ECON 205
PROBLEM SET 6 (Chapter 5-5.7)
1) Of nine executives in a business firm, four are married, three have never married, a
PROBLEM SET 7
1) The pdf of X is given as
6(1 )
0< <1
() = cfw_
0
a) Find the pdf of the random variable Y which is defined as = 2 + 1
b) Find the probability density of Y=X3
2) Let X and Y be two ind
Middle East Technical University
Department of Economics
SPRING 2013-2014
ECON 205
PROBLEM SET 1(CHAPTER 2)
1) Consider a universal set such that S=cfw_1,2,3,4,5,6. Answer the following
a)How many sub
ECON205
Problem Set 7
2013-2014 Fall
6x(1 x), 0 x 1
0,
otherwise
a) Find the pdf of the random variable Y which is dened as Y = 2X + 1
b) Find the probability density of Y = X 3
1)
f (x) =
2) Let X an
PROBLEM SET 7
1) The pdf of X is given as
f (x)= 6 x ( 1x ) 0< x <1
0 elsewhere
cfw_
a) Find the pdf of the random variable Y which is defined as
Y =2 X +1
b) Find the probability density of Y=X3
2) L
Middle East Technical University
Department of Economics
SPRING 2013-2014
ECON 205
Due Date: April 7th 2014, 17:00
HOMEWORK I (CHAPTERS 2&3)
1) Two balanced dice are rolled, one is red and one is gree
Middle East Technical University
Department of Economics
SPRING 2013-2014
ECON 205
Due Date: May 9th 2014, 17:00
HOMEWORK 2
1) X is a continuous random variable that follows the uniform distribution o
Country
Austria
Austria
Austria
Austria
Austria
Austria
Austria
Austria
Austria
Austria
Austria
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Belgium
Bulgaria
Bulgari
10 The F distribution and its uses
10.1 Introduction
In section 5.2 we discussed the sampling distribution of the means
of samples taken from the same population, and in section 7.2 we
extended the
Middle East Technical University
Department of Economics
Fall 2016-2017
ECON 205
ERDL, AKD
PROBLEM SET 7
1) The pdf of X is given as
6(1 )
0<1
() = cfw_
0
a) Find the pdf of the random variable Y whic
OrderDate
Region
6/1/2014 East
1.23.14
Central
9/2/2014 Central
2.26.14
Central
3.15.14
West
1/4/2014 East
4.18.14
Central
5/5/2014 Central
5.22.14
West
8/6/2014 East
6.25.14
Central
12/7/2014 East
7.
STATISTICAL ANALYSIS OF LEVEL OF
DEVELOPMENT IN REPUBLIC OF CYPRUS
Information about my dataset
My data comes from Republic of Cyprus Statistical
Service.
This data include national acoounts from 1995
University of California, Los Angeles
Department of Statistics
Statistics 100A
Instructor: Nicolas Christou
Some special discrete probability distributions
Bernoulli random variable:
It is a variable
Middle East Technical University
Department of Economics
Fall 2014-2015
ECON 205
ERDL, AKD
PROBLEM SET 5
1) Suppose that a radioactive particle is randomly located in a square with sides of unit
lengt
Middle East Technical University
Department of Economics
Fall 2014-2015
ECON 205
ERDL, AKD
PROBLEM SET 7
1. A random variable Y with probability density function given by
Use the method of transformat
Middle East Technical University
Department of Economics
Fall 2014-2015
ECON 205
ERDL, AKD
PROBLEM SET 7
1. A random variable Y with probability density function given by
Use the method of transformat
Middle East Technical University
Department of Economics
Fall 2014-2015
ECON 205
ERDL, AKD
PROBLEM SET 6
1) For a continuous example, where X is the weight of almonds and Y is the weight of
cashews in