# hw2 - EE595A Introduction to Information Theory Winter 2004...

This preview shows pages 1–2. Sign up to view the full content.

EE595A Introduction to Information Theory University of Washington Winter 2004 Dept. of Electrical Engineering Handout 4: Problem Set 2 Prof: Jeff A. Bilmes Lecture 6, Jan 26, 2004 DUE: Wednesday, Feb 4th, 2004, in class Book Problems Problem 1: Let S be a random variable with a binomial distribution with parameters n and p so that P ( S = i ) = ± n i ² p i (1 - p ) n - i show that the most likely value of S is the value <np> , where <np> is the integer closest to np . Hint: use the fact that P ( S = i + 1) P ( S = i ) = ( n - i ) p ( i + 1)(1 - p ) and consider the cases when i < np , and i > np . Problem 2: Consider a sphere of radius r in N dimensions. Show that the fraction of the volume of the sphere that lies at values of the radius between r - ± and r , where 0 < ± < r , is: f = 1 - ³ 1 - ± r ´ N . Using matlab, evaluate f for the cases N = 2 ,N = 10 , and N = 1000 with a) ±/r = 0 . 01 ; and b) ±/r = 0 . 5 . Notice that points that are uniformly distributed in a sphere in N dimensions are very likely to be in a thin shell near the surface when N is large. Note that you might find useful the volume of a hypersphere of radius

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw2 - EE595A Introduction to Information Theory Winter 2004...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online