IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Practice Midterm Exam October 7, 2008 Page 1 of 10
Practice Midterm Exam
Place all answers on the question sheet provided. The exam is open book/notes/handouts/homework. You are allowed to use a calculato
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Midterm Exam October 23, 2008 Page 1 of 11
Midterm Exam
Place all answers on the question sheet provided. The exam is open book/notes/handouts/homework. You are allowed to use a calculator, but not a comp
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #10 Solutions December 16, 2008 Page 1 of 3
Assignment #10 Solutions
1. Based on MATLAB output, we choose the following two candidate distributions: Normal Lognormal We rst use the Kolmogorov-S
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Solutions to the Practice Midterm Exam October 15, 2008 Page 1 of 10
Solutions to the Practice Midterm Exam
Place all answers on the question sheet provided. The exam is open book/notes/handouts/homework.
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #8 November 11, 2008 Page 1 of 2
Assignment #8 due November 18th, 2008
1. Suppose that Y1 , Y2 , . . . is an output process with steady-state mean and that Y (n) is the usual sample mean based
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Practice Final Exam December 8, 2008 Page 1 of 13
Practice Final Exam
This exam is open book/notes/handouts/homework. You are allowed to use a calculator, but not a computer. Write all answers clearly and
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #9 November 21, 2008 Page 1 of 2
Assignment #9 due November 25th, 2008
1. Five elements, numbered 1, 2, 3, 4, 5, are initially arranged in a random order (i.e., the initial ordering is a random
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #5 October 7, 2008 Page 1 of 1
Assignment #5 due October 14th, 2008
1. Buses arrive at a sporting event according to a Poisson process with rate 5 per hour. Each bus is equally likely to contai
IEOR 4404 : Homework 4
1. Binomial Lattice Model (BLM): Sn+1 = Sn Yn+1 , n 0. Suppose that S0 = 50 (dollars
per share), u = 1.3, d = .90, and p = 0.6.
(a) For T = 20, and K = 60, you are to estimate the expected payoff E(CT ) of an Asian
call option, with
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #5 Solutions October 22, 2008 Page 1 of 3
Assignment #5 Solutions
1. Algorithm: Let I be the number of arrivals of buses that have occurred by time T = 1, Bi be the number of fans in the ith bu
IEOR 4404 Homework 3
1. TEXT, Page 94, Exercise 20. (HINT: Consider g(x) = ex , for an aproppriate
value of .)
2. Program up simulating a Poisson point process cfw_tn : n 1 up to a desired time
T > 0 via using the fact that conditional on N (T ) = n, the
IEOR 4404 Lecture 2: Probability Review
Yuan Zhong
IEOR, Columbia U
Outline
Probability space
Conditioning and independence
Random variables discrete and continuous
Expectation (and variance)
Some well-known random variables (next time)
Probability Space
IEOR 4404 Lecture 10: Acceptance Rejection
Continued
Yuan Zhong
IEOR, Columbia U
Last lecture
Acceptance/rejection method
I
I
I
I
Broadly applicable way to generate complicated random variables
Idea: generating a complicated r.v using a related, simpler o
IEOR 4404: Homework 6
1. Consider the FIFO GI/GI/1 queue as a model for a printer which
prints one job at a
x
time according to the distribution G(x) = P (S x) = 1 e
, x 0 (service time
distribution), and jobs arrive according to a renewal process with ii
c 2016 by Karl Sigman
Copyright
1
Non-stationary Poisson processes and Compound (batch) Poisson processes
Assuming that a Poisson process has a fixed and constant rate over all time limits its applicability. (This is known as a time-stationary or time-ho
IEOR 4404 Homework 2 Solutions
1. Program up our alternative algorithm for simulating a Poisson rv X with mean
.
k
P (X = k) = e , k 0.
k!
Here is the Pseudo Code:
Alternative algorithm for generating a Poisson rv X with mean :
i Enter desired > 0. Set X
IEOR 4404 Homework 1 Solutions
Let U be uniformly distributed on the interval (0, 1); P (U x) = x, x (0, 1). We assume that your computer can sequentially generate such U independently upon demand.
1. Show that U and V = 1 U are negatively correlated with
IEOR 4404 Homework 1
Let U be uniformly distributed on the interval (0, 1); P (U x) = x, x (0, 1). We assume that your computer can sequentially generate such U independently upon demand.
1. Show that U and V = 1 U are negatively correlated with correlati
IEOR 4404 Homework 2
1. Program up our alternative algorithm for simulating a Poisson rv X with mean
.
k
P (X = k) = e , k 0.
k!
Here is the Pseudo Code:
Alternative algorithm for generating a Poisson rv X with mean :
i Enter desired > 0. Set X = 0, P = 1
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #6 October 20, 2008 Page 1 of 1
Assignment #6 due October 28th, 2008
1. Suppose in the insurance risk model presented in Lecture 11 that, conditional on the event that the rms capital goes nega
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #6 Solutions 2nd November 2008 Page 1 of 4
Assignment #6 Solutions
1. Here, all you have to do is use the algorithm given in class and modify it very slightly: using the same notations as the l
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #7 October 29, 2008 Page 1 of 2
Assignment #7 due November 6th, 2008
1. Estimate, using the method described in Lecture 14, the worth of owning an option to sell a stock anytime in the next 20
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #7 Solutions 15th November 2008 Page 1 of 7
Assignment #7 Solutions
1. Here is the code for pricing the American option. The simulation point estimate for the price is approximately equal to 14
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #8 Solutions November 20, 2008 Page 1
Assignment #8 Solutions
1. Assuming cfw_Yi , i = 1, 2, . . . are dened as Yi = ()i where (0, 1), then the steady-state is
n
lim Yn = 0
and the steady-state
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #9 Solutions December 6, 2008 Page 1
Assignment #9 Solutions
1. Five elements, numbered 1, 2, 3, 4, 5, are initially arranged in a random order (i.e., the initial ordering is a random permutati
IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto
Assignment #10 November 25, 2008 Page 1 of 3
Assignment #10 due December 8th, 2008
1. Download the text le Data1.txt and import it into MATLAB by typing > Data = csvread(Data1.txt) The vector Data is a sa