Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Solution to Exercise 2.28:
The purpose of this problem is to illustrate that for an arrival process with independent
but not i
M SS CHUSETTS INSTITUTE OF TECHNOLOGY
Fall 2007
Final exam, 1:304:30pm, (180 mins/100 pts)
6.436J/15.085J
12/19/07
Problem 1: (24 points)
During the time interval [0, t], men and women arrive accordin
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Solution to Exercise 2.3:
a Given Sn = , we see that N (t) = n, for t only if there are no arrivals from to
t. Thus,
Pr (N (t)
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Solution to Exercise 2.28:
Suppose that the states are numbered so that state 1 to J1 are in the recurrent class 1,
J1 + 1 to
M SS CHUSETTS INSTITUTE OF TECHNOLOGY
Fall 2008
Final exam, 1:304:30pm, (180 mins/100 pts)
6.436J/15.085J
12/18/08
Whenever asked to explain or justify an answer, a formal proof is not needed, but
jus
6 436/15 085
Midterm Exam
Date: October 23, 2006
Problem Which of the following functions is a distribution function? For those which are
compute the density function. For those which are not explain
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Solution to Exercise 1.10:
a We know that Z(!) = X(!) + Y (!) for each ! 2 .
Pr(Z(!) = 1) = Prcfw_!; Z(!) = +1 or Z(!) =
!
= P
Solutions to Homework
6.262 Discrete Stochastics Process
MIT Spring 2011
Solution to Exercise 1.3:
a Since A , A2 , . . . , are assumed to be disjoint, the third axiom of probability says that
1
X
[1
6.262 Discrete Stochastic Processes
MIT, Fall 2011
Monday April 4, 7:00-9:30pm, 2011
Solutions to Quiz
Problem 1: An innite sequence of packets are waiting to be sent, one after the other,
from point
Solutions to Homework
6.262 Discrete Stochastic Processes
MIT Spring 2011
Exercise 1
Let cfw_Yn ; n 1 be a sequence of rvs and assume that limn!1 [|Yn |] = 0. Show that
cfw_Yn ; n 1 converges to 0 in