Mathematics for Computer Science

18.8. Really Great Expectations 653 (c)Gallup actually claims greater than 99% confidence in his estimate. How might he have arr ...

Chapter 18 Deviation from the Mean654 is sufficient to be so confident. Suppose you were were the defendent. How would you expla ...

18.8. Really Great Expectations 655 The editors of the Journal reason that under this policy, their readership can be confident ...

Chapter 18 Deviation from the Mean656 Given that the last line in theprogramis buggy, the probability that the next- to-last li ...

18.8. Really Great Expectations 657 (b)Upper bound the probability that I forget one or more items. Make no inde- pendence assum ...

Chapter 18 Deviation from the Mean658 super bond can then be itself separated into tranches, which are again ordered to indicate ...

18.8. Really Great Expectations 659 (b)Conclude that PrŒonly finitely manyAn’s occurçD 0. Hint:LetCkbe the event that noAnwithn ...

Chapter 18 Deviation from the Mean660 Class Problems Problem 18.22. You have a biased coin with nonzero probabilityp < 1of co ...

19 Random Processes Random Walksare used to model situations in which an object moves in a sequence of steps in randomly chosen ...

Chapter 19 Random Processes662 capital gambler’s n T = n + m time bet outcomes: WLLWLWWLLL Figure 19.1 A graph of the gambler’s ...

19.1. Gamblers’ Ruin 663 T D 100 C 500 D 600. The probability of Albert winning is500=600D5=6, namely, the ratio of his wealth t ...

Chapter 19 Random Processes664 expectations of his payoffs of each bet, namely 0. Here we’re legitimately appeal- ing to infinit ...

19.1. Gamblers’ Ruin 665 Corollary 19.1.2.In the Gambler’s Ruin game with initial capital,n, target,T, and probabilityp < 1=2 ...

Chapter 19 Random Processes666 w n 0 downward drift gambler’s wealth time upward swing (too late) Figure 19.2 In a biased random ...

19.2. Random Walks on Graphs 667 Proof. If the gambler has initial capitalnand goes broke in a game without reach- ing a targetT ...

Chapter 19 Random Processes668 But in 1995, two students at Stanford, Larry Page and indexBrin, Sergey Sergey Brin realized that ...

19.2. Random Walks on Graphs 669 pages with links to your page. +n There is another problem —a page could become unfairly influe ...

Chapter 19 Random Processes670 For example, if the user is at pagex, and there are three links from pagex, then each link is fol ...

19.2. Random Walks on Graphs 671 19.2.3 Stationary Distribution & Page Rank The basic idea of page rank is just a stationary ...

Chapter 19 Random Processes672 Now just keeping track of the digraph whose vertices are billions of web pages is a daunting task ...