Please send homework solutions and questions to TA.
Homework 1 (Basic Probability) Due Tuesday Feb 19, 2011
Problems: 2.6, 2.8, 2.11, 2.14, 2.21, 2,23.
Problems: 3.38, 3.2, 3.15, 3.17, 3.26.
Homework 2 (Discrete Random Variables and Distributions)
Due Tuesday March 5
Problems: 2.19, 2.20.
Problems: 3.20, 3.22, 3.25, 3.27, 3.29, 3.32, 3.34, 3.35, 3.36.
Homework 3 (Continous Random Variables and
uniform, exponmential, Gamma Distributions,
Normal Distribution and Central Limit Theorem).
Due Thurs March 21
Problems: 4.5, 4.6, 4.7, 4.8, 4.10, 4.11. 4.14, 4.16, 4.22.
Problems: 4.17, 4.18, 4.21
Homework 4 (Computer Simulation, Markov Process, Stochastic Process,
Parameter Estimation).
Due Thurs April 11
Problems: 5.1, 5.4, 5.6, 5.15
Problems: 6.3, 6.4, 6.7, 6.9, 6.15
Problems: 9.1 , 9.4, 9.5.
Homework 5 (Hidden Markov Models).
Due Thurs May 2
These refer to the tutorial by L.R. Rabiner.
Problem 1: Prove Eq.27 using the definition of gamma (the optimal estimation of hidden state).
Problem 2: Using the definition of Eq.36, prove Eq.37.
Problem 3: The flow balance of a Markov chain:
probability go into site i = \sum_j \pi_j P_{ji}
probability go out of site i = \sum_k \pi_j P_{jk}
Prove these two are equal.