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ProbabilityPart_1.2011_toBayes - ITI 111 Mor Naaman PhD and...

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ITI 111 Mor Naaman, PhD and Paul Kantor Probability Notes 03 Probability 1. Probability 1.1. Probability Intro and Motivation Wikipedia : A way of expressing knowledge or belief that an event will occur or has occurred If a fair coin is tossed, what is the prob ability of getting heads?‖ ―If a fair coin is tossed 10 times ; what is the probability of getting 8 heads?‖ In order to clarify the relation between the actions and the things that happen after those actions are taken, we are going to introduce one more term: experiment. This does not mean quite the same thing as an experiment in a chemistry lab. It is a technical way of referring to the action that has a random outcome. Outcomes, and Sample Spaces An experiment governed by chance has several possible outcomes The collection of all possible outcomes in an experiment is the sample space Example experiments: Tossing a coin Rolling a die Rolling two dice —Getting ten result pages for query ―sleeping baby‖ Example outcomes: Heads The first die shows a 4, and the second shows a 5 10 specific web pages (query results) in a specific order Corresponding Sample Spaces: --{Heads, Tails} -- All possible combinations of two die {(1,1), (1,2), (2,1), (1,3), (3,1),…(6,6)} -- All possible set of 10 different web pages 1.1.1. Probabilities In Web Search More details later, but a couple of examples on how we are going to use it:
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ITI 111 Mor Naaman, PhD and Paul Kantor Probability Notes 03 Probability * Estimates on how many result pages will be returned for each query * The Probability that a user who entered a given query will be satisfied by a specific document E.g. for each particular page that it might deliver, what fraction of the users will think "yes this is exactly what I want"? In this case we want to know statistics about all of the users who might enter the query terms: flying, lessons, Hawai‘i. A third concept: the probability that a web page that has a particular set of features (such as the words that are in it) will satisfy ―this particular user‖ who has just asked us a query. In this case we want to know more about the particular user. 1.1.2. Outcomes and events We will agree to use the general term Event = to mean ― a collection of possible outcomes in an experiment ‖. A die rolls 5 or higher It will rain tomorrow A student will be late today A student will get a grade better than B More than 15 students will get a B 7 or more web pages are relevant to the query 1.1.3. Elementary Events Elementary events can be counted, and are not composed of more elementary events. If the ―event‖ ―getting an even number from the set of Integers 10 E {2, 4, 6, 8, 10} elementary? No! Seeing an even numbers from 10 E is not elementary events, because it can happen in several different ways. The set containing nothing but 2, is elementary. You can‘t break it down any further. So the set containing the number ―2‖ is elementary in the set of numbers. But it is just one part of the set         0 2
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