Example: Condence Intervals
Stat 135 Fall 2014
(7.7.8) A sample of size 100 is taken from a population that has a proportion
p = 1/5.
a. Find such that P (| p| ) = 0.025
p
b. If, in the sample, p = 0.25, will the 95% condence interval for p contain
the tr

Statistics 154: Modern Statistical Prediction and Machine Learning
Welcome to Stats 154. Here is the syllabus.
Instructor: Nusrat Rabbee, rabbee@berkeley.edu. Office: 309 Evans.
Office hours: W 4-5, or after class or by appointment.
Graduate Student Instr

Stat 155 Fall 2014: Homework 1
1. Lost Springs population:
(a) The sample mean takes the values 52, 67, 72.5, and 59.5 (all in years), with an equal probability of 1/4.
(b) The sample mean is not unbiased: E(X) = 62.75, = 62.25
2. (7.4) The rst, since Var

Stat 155 Fall 2014: Solution to Homework 5
1.
There are three alternative procedures to determine the outcome of a criminal
court case:
Status Quo: First determine innocence or guilt; then, if guilty, consider
the appropriate punishment.
Roman Tradition

Stat 155 Fall 2009: Final Exam December 15, 2009
Solutions
Duration: 3 hours
Instructor: Shobhana Murali
Name:
Instructions: Please write your name at the top of every page. This exam has 9 problems, each worth 12 points,
please attempt them all. Write yo

Stat 155 Fall 2009: Final Exam, December 15, 2009
Duration: 3 hours
Instructor: Shobhana Murali
Name:
Instructions: Please write your name at the top of every page. This exam has 9 problems, each worth 12 points,
please attempt them all. Write your answer

Stat 135 Fall 2014 Lec 2
1. (a) z/2 s = 1.96
p
(b)
i.
ii.
iii.
iv.
v.
0.14.0.86
10171
MIDTERM EXAM SOLUTIONS
= 0.02133
False. Almost same FPC. FPC for CA = 0.999973, FPC for FL = 0.999946, hence False.
False. Need to quadraple.
False. Either in or out, so

Econ 101B: Economic Analysis Macroeconomics
Problem Set #4
Due Date: October 2nd, 2014
Please submit the homework before the class starts. Late homework will not be
accepted.
Please put your name, student ID & your GSIs name at the up right corner of th

Econ 101B: Economic Analysis Macroeconomics
Problem Set #3
Due Date: September 25th, 2014
1. The goal of this exercise is to estimate Okuns law using data from the Federal Reserve.
Download the following time-series from FRED:1
The civilian unemployment

Econ 101B: Economic Analysis Macroeconomics
Problem Set #2
Due Date: September 18th, 2014
1. In a closed economy, if GDP is USD 10,000 B/year, government purchases are USD
1,000 B/year and Investment is USD 3,000 B/year, what is the level of personal cons

Stat 135 Fall 2013
Midterm Exam: Answers
1. Consider a population consisting of ve values: 2, 4, 5, 5, 7.
(a) Write down all the 10 possible samples, and the corresponding sample means. So X has the following distribution:
x
P ( X = x)
11/3
0.2
4
0.1
13/3

C181InternationalTrade
Fall2014
AndrsRodrguezClare
Ricardian model: part 2
So far we have:
Solved for autarky equilibrium
Solved for trade patterns (for given international prices)
Examined the gains from trade
We still need to:
Solve for wages
Solve for

Econ C181, Lecture Notes on Comparative Advantage
(Preliminaries)
Andrs Rodrguez-Clare, UC Berkeley
February 4, 2014
Rodrguez-Clare ()
Endowment Economy
February 4, 2014
1 / 33
The Challenge
Nobel laureate Paul Samuelson (1969) was once challenged by the

Econ C181, Lecture 2: Endowment Model
Andrs Rodrguez-Clare, UC Berkeley
January 21, 2015
Rodrguez-Clare ()
Endowment Model
January 21, 2015
1 / 13
Basic assumptions
G goods, labeled g = 1, ., G .
Rodrguez-Clare ()
Endowment Model
January 21, 2015
2 / 13
B

Department of Economics
University of California, Berkeley
Spring 2015
Economics 181
Econ 181: International Trade
Prof. Andrs Rodrguez-Clare
e
Spring, 2015
Problem Set 1
January 29, 2015
Due on Thursday, February 5 beginning of lecture.
Please, write you

Taxable Income Elasticities
131 Undergraduate Public Economics
Emmanuel Saez
UC Berkeley
1
TAXABLE INCOME ELASTICITIES
Modern public nance literature focuses on taxable income
elasticities instead of hours/participation elasticities
Two main reasons:
1) W

Social Insurance: The New Function
of Government
131 Undergraduate Public Economics
Emmanuel Saez
UC Berkeley
1
DEFINITION
Social insurance programs: Government interventions in the
provision of insurance against adverse events:
Examples: (a) health insur

Econ 101B: Economic Theory Macroeconomics
Problem Set #1
Due Date: September 11, 2014
Please submit your homework before class starts: late homework will not be accepted.
Please put your name, student ID & your GSIs name at the up right corner of the
fr

C181 International Trade
Spring 2015
Andrs Rodrguez-Clare
In this chapter we will examine the following topics:
Ricardian model:
Derive PPF
Opportunity cost
No-trade equilibrium
Relative prices
Wages
Trade and arbitrage
Comparative advantage and ex

Math 116
Quiz 10
November 21, 2013
Name:
1. Which of the following is true about a normally distributed random variable X with parameters and
.
A. p(X ) = A( )
B. p(X ) = p(X + )
C. p(X 5) = A( 5 )
D. The area under the curve is A(1)
2. The incidence of c

Math 116
Quiz 8
October 31, 2013
Name:
1. [1 point] A basketball player makes free throws with probability .7. What is the probability of making
exactly 3 out of 5 free throws?
A.
B.
C.
D.
5
3
5
3
5
3
(5
3
0.73
5
2
0.73 0.32
0.73 0.32
+
5
2
) 0.73
2. [

Math 116
Quiz 9
November 14, 2013
Name:
1. Which of the following is true for all normally distributed random variables X with = 0?
A. p(X k ) = A(k )
B. p(X k ) = 1 A(k )
C. p(X k ) = p(X k )
D. Theyre all true
2. What is the probability that an outcome

Math 116
Quiz 7
October 24, 2013
Name:
1. Consider random variables X, Y with the following distributions:
k
1
2
3
4
p(X = k )
.30
.40
.20
.10
p(Y = k )
.20
.20
.20
.40
(a) [1 point]
A.
B.
C.
D.
What is the probability that Y 2 is at most 9?
1
.60
.40
.20

Math 116
Quiz 6
October 17, 2013
Name:
1. [1 point] Let B1 , B2 mutually exclusive events (with non-zero probability), A any event.
Which of the following isnt true in general?
A. B1 and B2 are dependent events
B. p(B1 ) p(A|B1 ) = p(A) p(B2 ) p(A|B2 )
C.

Math 116
Quiz 2
September 12, 2013
Name:
John has 5 ties, 10 shirts and 3 jackets.
2 ties are grey (but dierent shades), the other 3 are coloured.
5 shirts are grey (dierent shades again), the other 5 are coloured.
1. [2 points] How many ways can he hang

Math 116
Quiz 3
September 19, 2013
Name:
1. [1 point] You, a friend and three others are seated in a row for a picture. How many arrangements are
there if you sit next to your friend?
A. 5!
B. 4 3!
C. 4 2! 3!
D. 2! 3!
2. [1 point] What is the coecient of

Math 116
Quiz 4
September 26, 2013
Name:
1. [1 point] How many ways can we hand out 4 chocolate, 4 vanilla and 4 strawberry ice creams to 16
children, if no child gets more than one ice cream?
A.
B.
C.
D.
12!
4!4!4!
16!
1
4! 4!4
16!
4!4
12!
1
3! 4!3
2. [1