Econ 41 (Fall 2016)
Department of Economics, UCLA
Instructor: Shuyang Sheng
Homework 1
Due: October 3, in class
1. 1.1-2
2. 1.1-4
3. 1.1-6
4. 1.1-7
5. Toss a fair coin twice. A is the event "two tails", and B is the event "two heads". Are
A and B mutually
ECON 41 - STATISTICS FOR ECONOMISTS
(Winter, 2014)
UCLA Department of Economics
Zhipeng Liao
Contact: Instructors contacts are (310) 794-5427 and [email protected]
E-Mails: Due to the large number of students in the class, I do not guarantee res
Econ 41 (Winter 2014)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Supplemental Notes 1
In this notes, we will discuss and show the following formula in detail
n
(a + b)
=
n
X
n r r
b
n Cr a
r=0
=
n 0 0
b
n C0 a
+ n C1 an
1 1
b +
1 n 1
1a b
+ n
Econ 41 (Winter 2014)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Supplemental Notes 2
Example 1 (The Monty Hall Problem) Suppose you on a game show, and you given the
re
re
choice of three doors: Behind one door is a car; behind the others, go
Econ 41 (Winter 2014)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Supplemental Notes 3
In this supplemental notes, we illustrate the dierences and relations between the probability
mass function (p.m.f.) and cumulative distribution function (C.
Econ 41 (Winter 2014)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Lecture 3: Conditional Probability
Denition 1 The conditional probability of an event A given that event B has occurred is dened
by
P (A \ B)
P ( Aj B) =
P (B)
provided that P (B
Econ 41 (Winter 2014)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Practice Exam-2
1
Single Choice Problems
7. Suppose that we have a random sample fX1 ; X2 ; :; Xn g which has the following p.d.f.
( p p
1 ; if 0
x c
x
f (x) =
otherwise
0;
where
Econ 41 (Spring 2015)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Middle Term Exam (Version A)
The problems in this section only have one correct answer among the choices a, b, c and d. For
each problem, you will get 1 credit if your choice is
Sample for X
Sample for Y
Sample size for X
Sample size for Y
Sample mean (X)
Sample mean (Y)
Sample Variance (X)
Sample Variance (Y)
Pooled Sample Standard Deviation
Lower bound of CI:
Upper bound of CI:
649
699
12
16
712.25
705.4375
29957.8409
20082.129
Econ 41 Week 2
Ruoyao Shi
October 14th, 2014
Methods of Enumeration
Multiplication principle
n total possible outcomes, r procedures
with Replacement
without Replacement
Ordered
nr
n Pr
Unordered
n Cr
Exercise
1.2-5
Some albatrosses return to the worlds
ECON 41 : Week 6
Hyo Sang Kim
November 9, 2014
2.4
Estimation
So far, we learned how to compute probabilities, and how to compute mean and variance given
a distribution and its parameters. In practice, however, we usually do not know the parameters
of a d
ECON 41 : Week 7
Hyo Sang Kim
November 17, 2014
3.2
Continuous Probability Distributions
Denition [Probability Density Function (p.d.f.)] An integrable function f (x) is a probability density function of a continuous random variable X with support S if it
ECON 41 : Week 5
Hyo Sang Kim
November 2, 2014
2.3
Special Discrete Distributions
Denition [c.d.f.] The cumulative distribution function (c.d.f.) of a random variable X is
dened by
F (x) = P (X x)
2.3.1
Binomial Distribution
Suppose we repeat a certain ex
ECON 41 : Week 4
Hyo Sang Kim
October 26, 2014
2
Discrete Distributions
2.1
Discrete Probability Distributions
Denition [Random Variable] Consider an outcome space of a random experiment. A random variable is a real valued function dened on that outcome s
Click to edit Understand style
Using Games toMaster titleIncentives
Game theory models strategic behavior by agents think about how other agents may
behave and how that should influence ones own choice. It is where the players think
strategically.
Usefu
Joonmo Kang
Economics 41
Fall 2011
Handout Week 8
Summary of Statistical Facts and Confidence Intervals
Summary of Necessary Theoretical Results
Just review the result needed. Proofs are omitted.
Theorem 1 Let X1 , , Xn be n independent chi-square random
Handout for TA session 41-2: Week 4
Yi Chen, Oct.181
A. Special Discrete Distributions
Concepts:
Bernoulli Distribution: A Bernoulli trial is an experiment with two, and only two possible outcome.
A variable X has a Bernoulli (p) distribution if:
X=
(
1 w
Joonmo Kang
[email protected]
Economics 41
Statistics for Economists
UCLA
Fall 2011
Handout Week 5
Special Discrete Distributions, Estimation and
Linear Functions of Independent Random Variables
Before starting, Ill introduce THE VERY MOST IMPORTANT co
Econ 41 (Fall 2016)
Department of Economics, UCLA
Instructor: Shuyang Sheng
Homework 2
Due: October 10, in class
1. 1.2-2
2. 1.2-3
3. 1.2-9
4. Three dierent economics books, two dierent mathematics books, and one physics
book are to be arranged on a books
Econ 41 (Fall 2016)
Department of Economics, UCLA
Instructor: Shuyang Sheng
Homework 5
Due: October 31, in class
1. 2.2-3.
2. 2.2-4.
3. 2.2-7 (a), (b), (c).
4. A family has 4 natural children and has adopted 2 girls. Each natural child has equal
probabili
Econ 41 (Fall 2016)
Department of Economics, UCLA
Instructor: Shuyang Sheng
Homework 4
Due: October 24, in class
1. 2.1-1.
2. 2.1-2.
3. 2.1-3. Hint: Use
4. 2.1-7.
P
x
f (x) = 1:
5. 2.2-2.
6. A power utility can supply electricity to a city from 4 dierent
Econ 41 (Fall 2016)
Department of Economics, UCLA
Instructor: Shuyang Sheng
Homework 3
Due: October 17, in class
1. 1.3-4
2. 1.3-6
3. 1.3-8, but with a small change: The store had 10 cartons of milk, and 1 of them were
sour.
4. 1.4-2
5. 1.4-3
6. 1.4-9
7.
Econ 41 (Winter 2015)
Department of Economics, UCLA
Instructor: Zhipeng Liao
Practice Exam-2
1
Multiple Choice Problems
The problems in this section only has one correct answer among the choices a, b, c and d. You will
get 1 credit if your choice is corre
Handout for TA session 41-2: Week 10
Yi Chen, Nov.291
A. Basic Tests Concerning One Parameter
p value: In principle, tests concerning one parameter is the same as test of the hypothesis.
And using p value is just another side of the coin - we can compute
Joonmo Kang
Economics 41
Fall 2011
Handout Week 9
Confidence Intervals and Tests of Hypotheses
Basic Tests Concerning One Parameter
Confidence Intervals and Tests of Hypothesis
Basically, there are three kinds of statistical inference: point estimation, s
Joonmo Kang
Economics 41
Fall 2011
Handout Week 7
Normal distribution, CLT, Approximation and Summary of all
1
Normal distribution
The normal distribution is the most important distribution in statistical applications since many
estimators have approximat
Handout for TA session 41-2: Week 6
Yi Chen, Nov.11
A. Normal Distribution
Concepts:
Normal Distribution: The random variable X has a normal distribution N
1
f (x) = p
2
It has mean
2
and variance
distribution, with c.d.f.
exp
"
(x
)
2
2
2
#
;
2
if its p.
Joonmo Kang
[email protected]
Economics 41
Statistics for Economists
UCLA
Fall 2011
Handout Week 4
Bayess Theorem, Discrete Probability Distributions, and Expectation
Bayess Theorem
Bayess theorem is closely related to the conditional probability. Actu
Handout for TA session 41-2: Week 5
Yi Chen, Oct.251
A. Continuous Distribution Function
Concepts:
Probability Density Function (p.d.f.): The probability density function" of a random variable of
the continuous type, with space S that is an interval or un