3. If X and Y are independent the Cov(X,Y)=0
4. 1. limit F(y)=F(-infinity)=0
2. limit F(y)=F(infinity)=1
3.F(y) is a non-decr
Lab 1AExcel Version
Some Basic Growth Facts
This introductory lab will serve two purposes. First, it will acquaint you with some basic growth
facts that you will seek to explain later in the semester. Second, it will refresh your memory
buchstabieren: to spell
der Buchstabe: letter
groer Buchstabe: capital letter
kleiner Buchstabe:small letter
Aussprache des Buchstaben/ Pronunciation of Letter Beispiele/ Examples
sounds similar to the e in melon
sounds similar to the i i
Homework Week 6-7
1. (WMS 5.1 & 5.19) Contracts for two construction jobs are randomly assigned to one or more
of three firms, A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the
number of contracts assigned t
Statistics for Economists
Spring 2012, Heather F. Howard
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Show Your Work:
Answer each question completely showing
1) Short Answer: Give an intuitive explanation for the following questions. Your
answer to each question should be 1-3 sentences long and should not include
a) (2 points) What does it mean fortwo sets to be mutually exclusive?
Homework 1 Solutions
Exercise 1 Sketch the graphs of the following functions:
Solution. (a) y = ex
(b) y = ex
(c) y = ln x
Exercise 2 Find the derivatives of the following functions:
(b) x 3
(4+x2 ) 2
Are we consuming more today than we have in the past? Specically I want to
address whether or not we have devoted a greater portion of our income to consumption
in the past thirty years than in the thirty year ti
Econ 378: Data Analysis Project
The purpose of this project is to apply the principles of hypothesis testing to a
relevant, interesting economic question of your choosing. You will propose the
question, conduct a two-variable hypothesis tes
Homework Week 9
1. (WMS 5.96) Suppose that the random variables Y1 and Y2 have means 1 and 2 and
variances 12 and 22 respectively. Use the basic definition of the covariance of two
random variables to establish that:
a.) Cov(Y1, Y2) = Cov
Homework Week 1
Part 1 - Math Review
1. Evaluate the following factorial function. (Hint: The factorials are too big to evaluate in your
calculator. Simplify first)
109 108 107 106
2. Write out the followi
Homework Week 4
Discrete Random Variables
1. (WMS 3.12) Let Y be a random variable with p(y) given in the accompanying table.
Find E(Y), E(1/Y), E(Y2-1), and V(Y).
Answer: E(Y) = 1(.4) + 2(.3) + 3(.2) + 4(.1) =
Chapter 6: Functions of Random Variables
6.1 The distribution function of Y is FY ( y ) = 2(1 t )dt = 2 y y 2 , 0 y 1.
a. FU1 (u ) = P(U 1 u ) = P( 2Y 1 u ) = P(Y
u +1 2
+ + + ) = FY ( u2 1 ) = 2( u21 ) ( u2 1 ) 2 . Thus,
fU1 (u ) = FU1 (u ) = 1u , 1
Chapter 8: Estimation
Let B = B() . Then,
2 MSE ( ) = E ( ) 2 = E ( E ( ) + B ) 2 = E E () + E ( B 2 ) + 2 B E E () = V ( ) + B 2 .
a. The estimator is unbiased if E( ) = . Thus, B( ) = 0. b. E( ) = + 5.
a. Using Definition 8.3,
Chapter 2: Probability
2.1 A = cfw_FF, B = cfw_MM, C = cfw_MF, FM, MM. Then, AB = 0 , BC = cfw_MM, C B = / cfw_MF, FM, A B =cfw_FF,MM, A C = S, B C = C. a. AB b. A B c. A B d. ( A B ) ( A B )
Chapter 2: Probability
Homework Week 3
Part 1 Probability
1. (WMS 2.102) Diseases I and II are prevalent among people in a certain population. It is
assumed that 10% of the population will contract disease I during their lifetime, 15% will
contract disease II e
Homework Week 10
1. (WMS 7.11, 7.26) A forester studying the effects of fertilization on certain pine forests in
the Southeast is interested in estimating the average basal area of the pine trees.
a. In studying basal areas of similar tre
Homework Week 11
1. Suppose that E 1 E 2 and Var 1 12 , Var 2 22 . Consider the
estimator 3 a1 1 a 2
a. Show that 3 is an unbiased estimator for .
b. If 1 and 2 are independent, how should the constant a be chosen in order to
Homework Week 2
1. (WMS 2.42) A personnel director for a corporation has hired ten new engineers. If three
(distinctly different) positions are open at a Cleveland plant, in how many ways can she fill the
Answer: There are thre
Homework Week 12
1. (a-c only) suppose that Y1, Y2, ., Yn denote a random sample from the Poisson distribution
with mean .
a. Find the MLE for .
b. Find the expected value and variance of the estimator MLE .
c. Show the estimator MLE