AMS 570
Midterm Exam
Hongshik Ahn
March 25, 2014
NAME
Maximum possible score: 30 points
Show all work to obtain full credit.
1. Let X1 , X2 , . . . , Xn be a random sample from a distribution with cdf
Answers to Homework 3
AMS 570
3.13
EXT
=
xP (XT = x) =
x=1
=
x
x=1
1
P (X > 0)
P (X = x)
1
=
P (X > 0)
P (X > 0)
xP (X = x) =
x=0
xP (X = x)
x=1
EX
P (X > 0)
Similarly,
2
EXT =
EX 2
.
P (X > 0)
Thus,
7.22
This exercise will prove the assertions in Example 7.2.16, and more. Let
be a random
sample from a
population, and suppose that the prior distribution on is
.
Here we assume that
and are all know
AMS570
Prof. Wei Zhu
Point Estimators
Example 1. Let
be a random sample from
.
Please find a good point estimator for
Solutions.
There are the typical estimators for
estimators.
and
. Both are unbiase
Other Common Univariate Distributions
Dear students, besides the Normal, Bernoulli and Binomial distributions, the
following distributions are also very important in our studies.
1. Discrete Distribut
HW_1 _AMS_570
1.5 Approximately onethird of all human twins are identical (oneegg) and twothirds are fraternal (two egg) twins. Identical twins are necessarily the same sex,
with male and female bei
Other Common Univariate Distributions
Dear students, besides the Normal, Bernoulli and Binomial distributions, the
following distributions are also very important in our studies.
1. Discrete Distribut
AMS570 Lecture Notes #2
Review of Probability (continued)
Probability distributions.
(1)
Binomial distribution
Binomial Experiment:
1) It consists of n trials
2) Each trial results in 1 of 2 possible
AMS570
Professor Wei Zhu
1. Sampling from the Normal Population
*Example: We wish to estimate the distribution of heights of adult US male. It is believed that
the height of adult US male follows a no
AMS570.01
Final Exam
Spring, 2016
Name: _ ID: _ Signature: _
This is a close book exam. You are allowed a twosided 8x11 formula sheet. No cellphone or calculator or
computer of any kind is allowed. C
AMS570.01
Practice Final Exam
Spring, 2017
Name: _ ID:
_ Signature: _
Instruction: This is a close book exam. You are allowed a onepage 8x11 formula sheet (2sided). No cellphone or calculator
or comp
AMS570.01
Midterm Exam
Spring 2017
Name: _ ID: _ Signature: _
Instruction: This is a close book exam. You are allowed a onepage 8x11 formula sheet (2sided). No cellphone or calculator or computer is
AMS570.01
Practice Midterm Exam
Spring 2017
Name: _ ID:
_ Signature: _
Instruction: This is a close book exam. You are allowed a onepage 8x11 formula sheet (2sided). No cellphone or calculator
or com
AMS570
Order Statistics
1. Definition: Order Statistics of a sample.
Let X1, X2, ,
be a random sample from a population
with p.d.f. f(x). Then,
2. p.d.f.s for
W.L.O.G.(W thout Loss of Ge er l ty), let
The Poisson Process1
Let us assume that we are counting the occurrence of rare events over a period of time (or
distance, or volume, etc.). We will assume that for some constant > 0, the following
sta
Lecture 12
Data Reduction
We should think about the following questions carefully before
the "simplification" process:
Is there any loss of information due to summarization?
How to compare the amoun
AMS570 Lecture Notes #3
Review of Probability (continued)
(3)
Normal Distribution
Q. Who invented the normal distribution?
* Left: Abraham de Moivre (26 May 1667 in VitryleFranois, Champagne,
France
Power of the test & Likelihood Ratio Test
<Todays Topic>
Power Calculation (Inference on one population mean)
Likelihood Ratio Test (one population mean, normal
population)
You can watch this and othe
AMS 570
Professor Wei Zhu
Lecture 1
1. Review of Probability, the Monty Hall Problem
(http:/en.wikipedia.org/wiki/Monty_Hall_problem)
The Monty Hall problem is a probability puzzle loosely based on th
HW3 AMS 570
1. Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate
about 5% defective items. Let X be the number of defective items in a sample
without replacement of si
AMS570
Quiz 2
Name: _ID: _
Dear students: this is a closebook quiz, due at the end of our class, by 2:20pm.
1. Suppose
that
the
p.d.f.
,
of
the
random
variable
X
is
. Please Derive its mean and
varia
8.1
Let
of heads out of 1000. If the coin is fair, then
(
. So
)( ) ( )
Where a computer was used to do the calculation. For the binomial,
and
. A normal approximation is also very good for this
calc
A primer to bootstrapping;
and an overview of doBootstrap
Desmond C. Ong
Department of Psychology, Stanford University
August 22, 2014
Abstract
This primer is targeted mainly at psychologists in light
HW3 (Due Tuesday, February 22)
1. Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate
about 5% defective items. Let X be the number of defective items in a sample withou
AMS 570.1 Quiz 1 Name:
ID:
This is a close book exam. Please turn in by 2:20pm, the end of this lecture. Please
include detailed solutions for full credit.
1. As the lawyer for a client accused of mur
Solutions to HW_1 _AMS_570
1.5
a. A B C = cfw_a U.S. birth results in identical twins that are female
b. P (A B C) = 1/90 * 1/3 * 1/2 = 1/540
1.33
Using Bayes rule
P (MCB) =
=
1.41
a. P (dash sent 
Sol_HW_2_AMS 570
Q.1. Suppose that
and
are random variables with joint pdf
(
Find the pdf of
Set
)
cfw_
.
. So we get

Thus, J =

(
)
(
and U2 are independent.
)
(
(
And
) (
)
( )
(
), thus, U1
)
2.
Bootstrap Resampling
SPIDA
Toronto June, 2005
Bob Stine
Department of Statistics
The Wharton School of the University of Pennsylvania
wwwstat.wharton.upenn.edu/~stine
Plan for Talk
Ideas
Bootstrap vi
Inference on One Population Mean
Hypothesis Testing
Scenario 1. When the population is normal, and the
population variance is known
i .i .d .
Data : X 1 , X 2 , X n
~ N ( ,
Hypothesis test, for insta