Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 4.10: Consider a variation of an M/G/1 queueing system in which there is no
facility to save waiting customers. Assum
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 4.11
a From the gure, conditional on Sn = t
s (i.e., conditional on the age at time t being
s and on N (t) = n), the
6.262 Discrete Stochastic Processes
MIT, Spring 2011
Wednesday, May 18, 9:00-12:00 noon, 2011
Solutions to nal examination
Problem 1: A nal exam is started at time 0 for a class of n students. Each st
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Fall 2007
Midterm exam, 7-9pm, (120 mins/70 pts)
6.436J/15.085J
10/23/07
Possibly useful facts:
(a) If X is uniform on [a, b], then the variance of X is (b a)2 /1
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 1.22:
For each of the following random variables, nd the interval (r , r+ ) over which the moment generating function
Solutions to Homework 1
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 6.5:
Consider the Markov process illustrated below. The transitions are labelled by the rate
qij at which those tra
6.262 Discrete Stochastic Processes
MIT, Spring 2011
May 6, 2011, 2011
Solutions to practice problem set 12
Note: There is a minor error in the statement of Exercise 7.21, part b. The last equation
of
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 5.6:
Let cfw_Xn ; n
0 be a branching process with X0 = 1. Let Y , 2 be the mean and
variance of the number of o sprin
1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.262 Discrete Stochastic Processes
Midterm Exam - Solutions
April 7, 2009
Problem 1
1a) (i) Recall th
M SS CHUSETTS INSTITUTE OF TECHNOLOGY
Fall 2008
Midterm exam, 7-9pm (120 mins/100 pts)
6.436J/15.085J
10/21/08
Problem 1: (15 points)
Let cfw_Xn be a sequence of random variables (i.e., measurable fu