AMS572.01
Midterm Exam
Fall, 2014
Name _ID _Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please
provide complete solutions for full credit. The exam goes from 8:30 9:50am. Good luck!
1. Coffe
AMS572.01
Practice Final Exam
Fall, 201 3
Name _ID _Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete
solutions for full credit. The exam goes from 11:15am - 1:45pm. Good l
AMS572.01
Final Exam
Fall, 201 3
Name _ID _Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete
solutions for full credit. The exam goes from 11:15am - 1:45pm. (*Extended time
AMS572.01
Quiz 1
(Take home quiz, due Thursday 9/5/2013)
Fall 2013
1. A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face
shows up is exactly 1/6.
The dealer says: "You can choose your bet on a number, any
AMS572.01
Fall, 2013
Midterm Exam
Name _ID
_Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please
provide complete solutions for full credit. The exam is due at 11:20am. Please turn in this si
Homework #5 Solutions
Dear students, please try to work out these problems by yourself before looking at the solutions.
The homework problems are one population proportion: 9.1, 9.2, 9.4, 9.6, 9.9; two or more
population proportions: 9.11, 9.12, 9.19, 9.2
AMS572.01
Midterm Exam
Fall, 2013
Name _ID
_Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please
provide complete solutions for full credit. The exam is due at 11:20am. Please turn in this si
Homework #7 Solutions
Dear students, please try to work out these problems by yourself before looking at
the solutions. The homework problems are 10.4, 10.5, 10.6, 10.7, 10.8, 10.33, 10.34.
10.4
(a)
Next
90
80
70
60
50
40
1
2
3
Last
Yes.
(b)
The fitted le
AMS572.01
Extra Credit for the Midterm Exam
Fall, 2013
Name: _ ID: _ Signature:
_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions
for full credit. Good luck!
Version 1. To
Homework 1 Solution
1. Let and . Please prove that . Please do so using (1) the p.d.f. approach;
(2) the c.d.f. approach and (3) the m.g.f. approach. Please show the entire
derivation for full credit.
Solution:
(1) pdf approach:
Since , that is , then
,
s
AMS572.01
Quiz 5
Fall, 2013
Name: _ ID: _ Signature: _
Instruction: This is a take home exam due before class on Tuesday, October 8. Please type
the solutions in MS word. Good luck!
A group of babies all of whom weighed approximately the same at birth are
Inference on population mean(s)
1. One population mean
Point estimation / Confidence Interval / Test
Sample Size
Power
1) Normal population, is known
Exact test
2) Normal population, is unknown
3) Large sample
Exact test
Approximate test
4) (SAS) Nonparam
Homework #7 Solutions
Dear students, please try to work out these problems by yourself before looking at
the solutions. The homework problems are 10.4, 10.5, 10.6, 10.7, 10.8, 10.33, 10.34.
10.4
(a)
Next
90
80
70
60
50
40
1
2
3
Last
Yes.
(b)
The fitted le
Midterm #1, AMS572, Fall 2006
1. Arctic and Alpine Research investigated the relationship between the mean daily air
temperature and the cocoon temperature of woolybear caterpillars of the High Arctic.
(1) According to the data, can you conclude, at the s
AMS572.01
Midterm
Fall, 2007
Name: _ ID: _ Signature: _
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F.
Please provide complete solutions for full credit. The exam goes from 6:00-7:30pm. Good luck!
1 (for
AMS572.01
Midterm Exam
Fall, 2008
Name: _ ID: _ Signature: _
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide
complete solutions for full credit. The exam goes from 3:50-5:10pm. Good luck!
1
Lecture 12
Table of Continuous Distributions
Continuous
Probability density function
Mean
Variance
a+b
2
(ba)2
12
1
1
2
2
probability
distribution
Uniform
f (x) =
1
ba ,
a<x<b
0
other wise
ex
x>0
f (x) =
0
x<0
over (a, b)
Exponential
with
parameter
>0
N
AMS 572 Lecture Notes
Oct. 3, 2013.
Topic 1: Let W ~ k2 . W is indeed a special Gamma random variable.
Gamma distribution
X ~ gamma ( , ) (Some books use =
1
)
x
if f ( x) =
1
x 1e , 0 p x p
( )
or
f ( x) =
1=
r r 1 x
x e , 0 p x p if r is a non-negat
AMS572.01
Practice Midterm Exam
Fall, 201 3
Name _ID _Signature_
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete
solutions for full credit. *For the real midterm, we will have 3 pro
AMS 572 Class Notes
Chapter 12 Analysis of Variance (ANOVA)
One-way ANOVA (fixed factors)
* Goal: compare the means from a (a2) different populations.
* It is an extension of the pooled variance t-test.
* Assumptions:
(i) Equal (unknown) population varian
Simple Linear Regression:
1. Finding the equation of the line of best fit
Objectives: To find the equation of the least squares regression line of y on x.
Background and general principle
The aim of regression is to find the linear relationship between tw
AMS 507, Lecture 17
Chapter Eight: Limit Theorems
8.2 Chebyshevs Inequality and the Weak Law of Large Numbers
Proposition 2.1 Markovs inequality
If X is a random variable that takes only nonnegative values, then for any value a>0,
E[ X ]
Pcfw_ X a
.
a
Pr
AMS 507
Linear combinations of random variables can be written in vector notation as W = a T Y .
Then E[W ] = a T E[Y ] and var(W ) = a T vcv(Y )a, where
var(Y1 )
cov(Y1 , Y2 ) cov(Y1 , Yn )
vcv(Y ) =
cov(Y2 , Y1 )
var(Y2 )
cov(Y2 , Yn )
cov(Yn , Y1 ) co
Chapter Eight: Limit Theorems
Some Basic Facts
Proposition 2.1 Markovs inequality
If X is a random variable that takes only nonnegative values, then for any value a>0,
E[ X ]
Pcfw_ X a
.
a
Proposition 2.2 Chebyshevs inequality
If X is a random variable w
AMS 507
Chapter Six
Jointly Distributed Random Variables
6.3. Sums of Independent Random Variables
In a gambling problem, let X be the winnings from one play of a game of chance and
have pdf f X , and Y be the winnings from one play of another game of cha
AMS 507
Chapter Six: Jointly Distributed Random Variables
6.7. Joint Probability Distribution of Functions of Random Variables
Transformation of two random variables is a crucial problem and hard to handle. It is
important to review your multivariable cal
AMS 572 Data Analysis I
Basic Concepts of Inference
Pei-Fen Kuan
Applied Math and Stats, Stony Brook University
AMS 572
PF.Kuan
1
Sampling
AMS 572
I
A function of statistics is the provision of techniques for
making inductive inferences, i.e, generalizati
MS-E2114 Investment Science
Exercise 1/2015, Solutions
24.2.2016
General information:
Exercise sessions held Wed 10-12 and Fri 12-14 in room Y344.
Questions about exercises etc. [email protected]
First some theory:
The present value Px (r) of a cash o
AMS 572 Data Analysis I
Review of Probability
Pei-Fen Kuan
Applied Math and Stats, Stony Brook University
AMS 572
PF.Kuan
1
Course Info
AMS 572
I
Instructor: Pei-Fen Kuan, Ph.D, Office: Room 1-106 Math
Tower, Phone: (631) 632-1419
([email protected]