Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 1: Solutions
Due: February 15, 2006
1. (a) A B C
(b) (A B c C c ) (Ac B C c ) (Ac B c C) (A
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 6
Due: April 5, 2006
1. Suppose that
MX (s) =
1
1
2
3
+
.
3 1s 3 3s
What is the PDF of X?
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Solutions to Quiz 2: Spring 2006
Problem 1:(30 points)
Each of the following statements is either True
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Final Exam Solutions | Fall 2009)
Problem 3. (25 points)
(a) (5 points)
The recurrent states are cfw_3,4.
(b) (5 points
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Spring 2006)
Solutions to Final Exam: Spring 2006
Problem 1
(42 points, Each question is equally weighted at 3.5 points
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Spring 2006)
Solutions to Quiz 1: Spring 2006
Problem 1:
Each of the following statements is either True or False. Ther
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 4: Solutions
Due: March 8, 2006
1. (a) Use the total probability theorem by conditioning on
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 3
Due: March 1, 2006
1. Mary and Tom park their cars in an empty parking lot that consists
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 2
Due: February 22, 2006
1. Suppose that you were foolish enough to save your thesis on onl
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 6: Solutions
Due: April 5, 2006
1. X is the mixture of two exponential random variables wit
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 5 Solutions
Due: March 22, 2006
1. We are given that F () =
1
2
ex dx =
0
0
1
2
ex dx = ex
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 3: Solutions
Due: March 1, 2006
1. The problem did not explicitly state that two cars canno
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 1
Due: February 15, 2006
1. Express each of the following events in terms of the events A,
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 2: Solutions
Due: February 22, 2006
1. Let A be the event that your friend searches disk 1