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MIT6_01F09_lec09 - 6.01 Introduction to EECS 1 Week 9 6.01...

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6.01: Introduction to EECS 1 Week 9 November 3, 2009 6.01: Introduction to EECS I How can we look ahead when we don’t know where we are? Discrete Probability Uncertainty in results of actions Week 9 November 3, 2009 Let’s make a deal Types of State Spaces Atomic : states don’t have any further detailed structure. A state space described by one value from a list, e.g. (’closed’, ’closing’, ’open’, ’opening’) . A state space described by a single integer. A state space described by a single real number (infinite). Factored : a state is described by values of more than one (state) variable. A state space described by a seconds variable in { 0,...,59 } and a minutes variable in { 0,...,59 } . A state space described by X position and Y position (may be infinite). Uncertainty in results of sensing: What do we know when sonar number 2 returns a reading of 1.2? Probability Probability theory lets us Make precise statements about uncertainty Combine uncertain information to reach consistent (uncertain) conclusions Win bets State Spaces Single coin flip (atomic): { H, T } , Sequence of three coin flips (factored 3 variables): { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT } Randomly generated document (factored 1000 variables): all strings of 1000 words drawn from a particular dictionary . Robot navigating in a city (atomic): set of intersections in the city . Robot navigating in a city (factored 2 variables): GPS coordinates (longitude, latitude) . 1
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6.01: Introduction to EECS 1 Week 9 November 3, 2009 Probability Terminology Sample space analogous to state space Atomic events analogous to atomic states Random variables analogous to state variables, but also include a probability assignment. Events An event is a subset of the sample space U (the state space) con- taining zero or more atomic events (atomic states). An event in the three-coin-flip space: there are at least two heads: { HHH, HHT, HTH, THH } An event in the robot navigation space: the robot is within one mile of MIT . An event in the document space: the document contains, in sequence, the words ’6.01’ and ’rules’ .
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