Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Tutorial 3: Answers
March 23, 2006
1. (a)
24/90, s = 1;
36/90, s = 2;
pS (s) =
30/90, s = 3;
0,
oth
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Solutions for Recitation 21
Markov Chains: Absorption Probabilities and Expected Time to Absorption
May
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Recitation 10 Solutions
March 23, 2006
1. a) To nd the transform, we integrate the density function ove
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Recitation 12 Solutions
April 5, 2006
1. (a) First note that X should be a r.v., not a number. In part
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Recitation 08 Answers
March 09, 2006
1. (a) The marginal distributions are obtained by integrating the
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Recitation 2: Solutions
February 14, 2006
1. Problem 1.12, page 55 of text. See online solutions.
2. Pr
Probabilistic Systems Analysis and Applied Probability
EECS 6.041: B

Spring 2006
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Solutions for Problem Set 11:
Topic: Markov Processes
Due: May 12, 2006
1. (a) We dene a Markov chain w