Midterm Examination
Dynamical Systems Under Uncertainty (ECE272A)
Fall 2013
Ofce Hours: Monday 3:00-5:00pm, Atkinson Hall 4306 (additional Ofce Hours)
Honor Code: You are expected to take this exam under an honor code. No exam will be graded
unless the ex
ECE272A: Dynamical Systems Under Uncertainty
Fall 2013
Problem Set. 2 (Due October 29, 2013 )
Consider a MC with state spacecfw_0, 1, 2, 3, 4 with the following transition matrix:
0 1/3 2/3 0
0
0 0
0 1/4 3/4
0 0
0 1/4 3/4
P =
1 0
0
0
0
10
0
0
0
Show t
ECE 272A: Dynamical Systems Under Uncertainty
Fall 2013
Problem Set. 1: Solutions
Consider a MC with state spacecfw_0, 1, 2, 3, 4 with the following transition matrix:
0 1/3 2/3 0
0
0 0
0 1/4 3/4
0 1/4 3/4
P = 0 0
1 0
0
0
0
10
0
0
0
Show that the chai
ECE 272A: Dynamical Systems Under Uncertainty
Fall 2013
Problem Set. 1 (Due Oct 10, 2013)
1. Let Xn , n 0 be a M.C. Show that
P (X0 = x0 |X1 = x1 , X2 = x2 , . . . , Xn = xn ) = P (X0 = x0 |X1 = x1 )
(Markov property reversed in time).
2. (Pedestrian Lemm
ECE272A: Dynamical Systems Under Uncertainty
Fall 2013
Problem Set. 3 (Due November 21, 2013)
1. Suppose in a communication system we want to transmit I packets over a horizon of N time slots
(deadline). At each time slot, we allocate a certain amount of
ECE272A: Dynamical Systems Under Uncertainty
Fall 2013
Problem Set. 4 (Due Dec 5th 2013)
1. An individual has n tasks and no multi-tasking skills (tasks have to be done one at a time). Each
task i takes a random time Xi to complete and upon completion pro