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lecture19.pdf

# lecture19.pdf - COMPSCI 240 Reasoning Under Uncertainty...

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COMPSCI 240: Reasoning Under Uncertainty Arya Mazumdar University of Massachusetts at Amherst Fall 2016

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Lecture 19

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PageRank How can one rank the Web pages according to its relevance to a search query?
PageRank An important page has many links to it and can be reached easily.

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Cryptography Stanford’s Statistics Department has a drop-in consulting service. One day, a psychologist from the state prison system showed up with a collection of coded messages.
Cryptography Stanford’s Statistics Department has a drop-in consulting service. One day, a psychologist from the state prison system showed up with a collection of coded messages. What could be a feasible way to decode the passage?

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Cryptography Stanford’s Statistics Department has a drop-in consulting service. One day, a psychologist from the state prison system showed up with a collection of coded messages. Suppose the first symbol corresponds to ”A”. What is the probability that the next symbol is A/B/C/ .... /Z?
Markov Chain The future depends on past only through present! Example The web page that I will be visiting at time t + 1 given the visited web pages at time t , t - 1 , ..., 1, only depends on the web page visited at time t . Example Whether the next decoded symbol is ”B” only depends on the decoded symbol immediately preceding it. Example Whether you would understand the content of the next class only depends on whether you understand the concept in today’s class.

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Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe
Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . .

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Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . . I With probability 1 if the queue has length 0
Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . . I With probability 1 if the queue has length 0 I With probability 2 / 3 if the queue has length 1

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Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . . I With probability 1 if the queue has length 0 I With probability 2 / 3 if the queue has length 1 I With probability 1 / 3 if the queue has length 2
Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . . I With probability 1 if the queue has length 0 I With probability 2 / 3 if the queue has length 1 I With probability 1 / 3 if the queue has length 2 I With probability 0 if the queue has length 3.

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Analyzing the Queue at Earth Foods Cafe Consider a queue at Earth Foods Cafe Every minute, someone joins the queue. . .
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• Fall '12
• Ben
• Probability theory, Markov chain, Andrey Markov, Earth Foods Cafe

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