Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Spring 2006)
Solutions for Problem Set 2:
Topic: Central Limit Theorem
Due: No due date
1. It is not easy to calculate
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
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Final Exam Solutions | Fall 2010)
4. 4 points) Is the sequence Yn a Markov chain? Justify your answer.
Solution: No. As
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 12:
Topic: Central Limit Theorem
Due: No due date
1. The weight of a Pernotti Parabolic Pre
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 9
Topics: Bernoulli, Poisson
Due: May 3rd, 2006
1. Fred is giving out samples of dog food.
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 10
Topics: Poisson, Markov chains
Due: May 10th, 2006
1. (a) We are given that the previous
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Quiz 1 Solutions | Fall 2009)
P(ripe gala) = P(ripe gala | Calebs ripe gala)P(Calebs ripe gala)
+ P(ripe gala | k ga
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 8 Solutions
1. Let At (respectively, Bt ) be a Bernoulli random variable that is equal to 1
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(
)
Problem 1: True or False (2pts. each, 18 pts. total)
No partial credit will be given for individual questions in
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 9
Topics: Bernoulli, Poisson
Due: May 3rd, 2006
1. A successful call occurs with probabilit
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 7: Solutions
Due: April 12, 2006
1. For both parts (a) and (b) we will make use of the form
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Quiz 2 Solutions | Fall 2009)
(e) (7 points)
In the new universe in which X = 2, we are asked to compute the conditiona
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Quiz 2
lu i
| Fall 2010)
3. 10 points) Find the conditional joint PDF of X and Y , given that the event Y
occurred.
(Yo
Massachusetts nstitute of Technology
Department of Electrical Engineering & Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Quiz 1 Solutions| Spring 2009)
Question 1
Multiple Choice Questions: CLEARLY circle the appropriate choice. Scratch p
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2006)
Problem Set 8
Topics: Covariance, Estimation, Limit Theorems
Due: April 26, 2006
1. Consider n independ