# hw2 - ECE 5620 Spring 2011 Homework#2 Issued Feb 2 Due Feb...

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ECE 5620 Spring 2011 Homework #2: Issued Feb. 2, Due Feb. 18 at 5 p.m. Complete all ten problems. 1. Problem 16 in Chapter 2 of the text 2. Problem 25 in Chapter 2 of the text 3. Problem 29 in Chapter 2 of the text 4. Problem 12 in Chapter 3 of the text 5. Problem 8 in Chapter 7 of the text 6. Problem 9 in Chapter 7 of the text 7. Suppose that X 1 ,...,X n are independent. (a) Show that I ( X 1 ,...,X n ; Y ) n X i =1 I ( X i ; Y ) . (b) Give a collection of Markov chain conditions that is necessary and suf- ﬁcient for equality in (a). 8. Show that H ( Y | X ) is a concave function of the joint PMF p ( x,y ) . Is it strictly concave? 9. Let X 1 ,...,X n be i.i.d. Bernoulli( p ) and let Y 1 ,...,Y n be i.i.d. Bernoulli( q ). Show that - 1 n log p X ( Y 1 ,...,Y n ) converges in probability and determine the limit in terms of p and q . 10. Typical vs. Expected Behavior The Acahti Trust Company offers two investment instruments, the Lousy Money Market Account and the Risky Mutual Fund. After one year, the

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hw2 - ECE 5620 Spring 2011 Homework#2 Issued Feb 2 Due Feb...

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