Information Theory, Inference, and Learning ... - Inference Group

Copyright Cambridge University Press 2003. On-screen viewing permitted. Printing not permitted. http://www.cambridge.org/0521642981You can buy this book for 30 pounds or $50. See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links.About Chapter 50The following exercise provides a helpful background for digital fountain codes.⊲ Exercise 50.1. [3 ] An author proofreads his K = 700-page book by inspectingrandom pages. He makes N page-inspections, and does not take anyprecautions to avoid inspecting the same page twice.(a) After N = K page-inspections, what fraction of pages do you expecthave never been inspected?(b) After N > K page-inspections, what is the probability that one ormore pages have never been inspected?(c) Show that in order for the probability that all K pages have beeninspected to be 1 − δ, we require N ≃ K ln(K/δ) page-inspections.[This problem is commonly presented in terms of throwing N balls atrandom into K bins; what’s the probability that every bin gets at leastone ball?]588