UCSD ECE250
Prof. Young-Han Kim
Handout #1
Wednesday, January 6, 2016
Homework Set #1
1. Prove that H(p(x) is concave in p(x).
2. The total variation distance between two pmfs p(x) and q(x) is defined as
(p, q) =
1X
|p(x) q(x)|.
2
xX
(a) Show that this di
UCSD ECE287
Prof. Young-Han Kim
Handout #2
Wednesday, January 13, 2016
Homework Set #2
1. Let X = cfw_Xn be a stationary random process. Show that
H(X) = lim H(Xn |X n1 ).
n
2. Let Y = cfw_Yn be a stationary Markov chain and X = cfw_g(Yn ) be a hidden M
UCSD ECE287
Prof. Young-Han Kim
Handout #3
Wednesday, January 20, 2016
Homework Set #3
1. Let (q(xn ) be pointwise universal w.r.t. P, and u(xn ) 1/|X |n be the uniform probability
n=1
density. Show that (q (xn ) , where
n=1
q (xn ) =
1
n1
q(xn ) + u(xn )