550.171 - D ISCRETE M ATH
JHU S UMMER 2017
C OURSE S YLLABUS
Course Description
Discrete math is a fun and exciting branch of mathematics that is often overlooked
in high school curricula, which tend to focus primarily on continuous math building
up to ca
550.111 Statistical Analysis I - Fall 2012 @ 7 MIDTERM l
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Syllabus
Applied Mathematics and Statistics, 550.111
Statistical Analysis 1
Spring 2016
(4 credits, EQ)
Description: 550.111, Statistical Analysis I, provides a survey of descriptive and inferential statistical methods. Topics include descriptive statisti
Stat 111, Fall 2015: Topics and review problems for Exam 2
The topics and questions given here are meant as a guide to help you study for Midterm Exam II, which will
be on Wednesday, April 6, 2016. The actual exam may include some problems that are more d
Stat 111, Fall 2015: Topics and review problems for the Final Exam
THE FINAL EXAM FOR 550.111 WILL BE HELD ON
THURSDAY, MAY 12, 2016, FROM 2 P.M. TO 5 P.M.,
IN REMSEN HALL, ROOM 1.
The topics and questions given here are meant as a guide. It is not an exh
Stat 111, Spring 2016: Topics and review problems for Exam 1
The topics and questions given here are meant as a guide to help you study for Midterm Exam I, which will be
on Friday, February 26, 2016. The actual exam may include some problems that are more
Discrete Math Homework 8 Solutions
1. Let p, x, n Z with p prime and n > 0.
(a) Prove that if p | xn , then p | x.
Let p | xn , and suppose for sake of contradiction that p - x. Then, by the
Fundamental Theorem of Arithmetic, x = pe11 pe22 . . . pekk . Si
Discrete Mathematics (550.171)
Homework 9 (Due Friday, April 28, 2017)
General Directions: You must show all work and document any assumptions to receive
full credit. All problems are to be done by hand unless otherwise stated. Please see the
course sched
550.430, Fall 2016: Homework 3
Outline of Solutions
The homework is due at the beginning of class on Wednesday, September 28, 2016.
Please note: all Rice problems refer to the 3rd (US) edition. If this is not the edition you are usingfor
instance, if you
SAMPLE CHAPTER
The Little Elixir & OTP Guidebook
by Tan Wei Hao
Chapter 1
Copyright 2016 Manning Publications
brief contents
PART 1 GETTING STARTED WITH ELIXIR AND OTP.1
1
2
3
4
Introduction 3
A whirlwind tour 13
Processes 101 39
Writing server applicatio
550.420 Introduction to Probability - Spring 2017
Due Friday, Feb. 17 in lecture.
Homework #02
Do the following exercises from the course textbook:
Chapter 3 problems: 3.1, 3.5 , 3.11, 3.12 , 3.15, 3.30
these problems may require the use of the extended m
550.430, Fall 2016: Homework 1
The homework is due at the beginning of class on Wednesday, September 14, 2016. You are free
to talk with each other and get help. However, you should write up your own answers and understand
everything you write. You must s
Chapter 2
Descriptive methods for Time
series
When given time series data one shouid always perform the following operations: _
0 Plot the data. If possible, use varying aspect ratios this may highlight
interesting behaviors in the time series that would
Chapter 4
Some stationary time series
models
In this chapter we develop some basic time series models of stationarity (notation
and denitions) that will be the building biocks of some other extremely usefui
time series. '
In this chapter (Zt) N WN(0, 02)
Chapter 3
Stationary time series
3.1 Strict stationarity
(Xi)th is called strictly stationary provided
(XtZXl-Iav ' ' 1an) 2d (Xt1'+h-)Xt2+hi ' ' . ath+h)
for ali integers h, n 2 1, and 251,. . . ,tn,t1+h,. . .,tn+h E T. (md means equal in
distribution.)
5 mar MACW) ywm'bdxdh. .
W
h L
~ 1|.
ouhl 441 Un av'sk So WNW 5 prs > W)
J.
Y z in 79714, + cfw_t *Ji-.* qez.
B 6 -
Y- 3 .
- s _' _. .LT(k-L) 4 E(et\1,k)+ taq- H: .
o/(k) ' z k ) ( +$E(9.Jl-k\i
WC anqkyiL HNL luJr _,+L\r</ +Uw~r \oovt-
" M L 4 .
W k:0.) Y
CHAPTER 4
Interest Rates
Practice Questions
Problem 4.1.
A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is
the equivalent rate with (a) continuous compounding and (b) annual compounding?
(a) The rate with continuous c
550.445 Interest Rate & Credit Derivatives
Assignment
For February 10th thru February 15th (M3)
Convexity, Timing, and Quanto
Adjustments (M3)
o Read: Hull Chapter 30
o Homework 2: (Problems due Feb 13th)
o Chapter 29 (9e): 3, 14; 22, 25 a)
o Chapter 28
The dierence sign test for testing randomness.
Suppose Y1 , Y2 , . . . , Yn are i.i.d. with cdf F (x) which we will assume is a continuous function.
The dierence sign statistic is
n1
S=
I(Yi+1 > Yi ).
i=1
This statistic counts the number of times the dier
550.439 Time Series Analysis - Spring 2017
Due in lecture, Monday, February 20.
Homework #1
Do the following exercises from the course textbook:
Chapter 2: 2.4(a only), 2.7, 2.8, 2.9, 2.10, 2.17, 2.18 , 2.19.
in 2.18, what is labeled as part (d) is really
550.439 Time Series Analysis - Spring 2017
DUE: Friday, Feb. 10
Homework #0
1. (a) Download and install the R computing package on your computer - see the appendix of our textbook
(by Jonathan D. Cryer and Kung-Sik Chan*).
(b) Read chapter 1 of the textbo
550.426
Stochastic Processes
Biased Simple Random Walk
Biased Coin Tossing
Consider an infinite sequence of independent
biased coin tosses : P[ H ] p and P[T ] q 1-p
on each toss, where p q 1 and p q.
This situation could represent an unfair gambling
game
Markov Chains
Introduction
Markov Property (in discrete time)
Consider a stochastic process with positive
integer ti me parameter and state space N.
The process is a Markov Chain if :
For all n and every i0 , i1 , , in , and j in N,
P[ X n 1 j | X 0 i0 ,
Simple Symmetric Random Walk
Reference: Feller, Volume I, Chapter 3.
We will illustrate some important methods,
using the sample path (geometric) approach.
We will illustrate some of the important
concepts of stochastic processes.
Definition and Notation
Simple Symmetric Random Walk
Reference: Feller, Volume I, Chapter 3.
We will illustrate some important methods,
using the sample path (geometric) approach.
We will illustrate some of the important
concepts of stochastic processes.
Definition and Notation
Homework 1
550.426 Stochastic Processes
Spring 2017
Due Tuessday, February 7, 2017
[1] In a simple symmetric random walk, show that Sk and Sn , k = n, are dependent random variables.
Hint: Consider the covariance.
[2] Consider a gambler who on each gamble