This section contains lecture slides and video lectures. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures 2013-02-21T14:46:48+05:00 MIT OpenCourseWare http://ocw.mit.edu en-US Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed probability as a mathematical framework, probabilistic models, axioms of probability, and gave some simple examples.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: probability axioms, probability law, discrete uniform law, countable additivity axiom<br><br>Thumbnail - <a href= http://img.youtube.com/vi/j9WZyLZCBzs/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec01_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-1-probability-models/id577778306?i=123745364>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/j9WZyLZCBzs>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-1-probability-models-and-axioms Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US probability axioms probability law discrete uniform law countable additivity axiom MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed conditional probability, multiplication rule, total probability theorem, and Bayes' rule.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: conditional probability, die roll, multiplication rule, total probability theorem, Bayes' rule<br><br>Thumbnail - <a href= http://img.youtube.com/vi/TluTv5V0RmE/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec02_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-2-conditioning-bayes/id577778306?i=123745363>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/TluTv5V0RmE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-2-conditioning-and-bayes-rule Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US conditional probability die roll multiplication rule total probability theorem Bayes' rule MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed independence of two events, independence of a collection of events, and independence vs. pairwise independence.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: conditional independence, pairwise independence<br><br>Thumbnail - <a href= http://img.youtube.com/vi/19Ql_Q3l0GA/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec03_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-3-independence/id577778306?i=123745366>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/19Ql_Q3l0GA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-3-independence Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US conditional independence pairwise independence MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed principles of counting, permutations, combinations, partitions, and binomial probabilities.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: discrete uniform law, permutations, combinations, partitions, binomial probabilities<br><br>Thumbnail - <a href= http://img.youtube.com/vi/6oV3pKLgW2I/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec04_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-4-counting/id577778306?i=123745412>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/6oV3pKLgW2I>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-4-counting Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US discrete uniform law permutations combinations partitions binomial probabilities MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed random variables, probability mass function, expectation, and variance.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: random variables, probability mass function, expectation, variance<br><br>Thumbnail - <a href= http://img.youtube.com/vi/3MOahpLxj6A/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec05_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-5-discrete-random/id577778306?i=123745365>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/3MOahpLxj6A>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-5-discrete-variables-probability-expectations Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US random variables probability mass function expectation variance MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed conditional PMF, geometric PMF, total expectation theorem, and joint PMF of two random variables.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: conditional PMF, geometric PMF, total expectation theorem<br><br>Thumbnail - <a href= http://img.youtube.com/vi/-qCEoqpwjf4/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec06_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-6-discrete-random/id577778306?i=123745367>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/-qCEoqpwjf4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-6-discrete-random-variable-examples-joint-pmfs Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US conditional PMF geometric PMF total expectation theorem MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed multiple random variables, expectations, and binomial distribution.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: multiple random variables, expectations, binomial distribution<br><br>Thumbnail - <a href= http://img.youtube.com/vi/EObHWIEKGjA/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec07_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-7-discrete-random/id577778306?i=123745410>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/EObHWIEKGjA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-7-multiple-variables-expectations-independence Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US multiple random variables expectations binomial distribution MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed probability density functions, cumulative distribution functions, and normal random variables.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: probability density function, cumulative distribution functions, means and variances, normal random variables<br><br>Thumbnail - <a href= http://img.youtube.com/vi/mHfn_7ym6to/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec08_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-8-continuous-random/id577778306?i=123745414>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/mHfn_7ym6to>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-8-continuous-random-variables Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US probability density function cumulative distribution functions means and variances normal random variables MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed multiple random variables: conditioning and independence.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: probability density function, multiple random variable<br><br>Thumbnail - <a href= http://img.youtube.com/vi/CadZXGNauY0/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec09_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-9-multiple-continuous/id577778306?i=123745368>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/CadZXGNauY0>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-9-multiple-continuous-random-variables Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US probability density function multiple random variable MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Bayes rule, Bayes variations, derived distribution<br><br>Thumbnail - <a href= http://img.youtube.com/vi/H_k1w3cfny8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec10_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-10-continuous-bayes/id577778306?i=123745369>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/H_k1w3cfny8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-10-continuous-bayes-rule-derived-distributions Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Bayes rule Bayes variations derived distribution MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed derived distributions, convolution, covariance and correlation.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Derived distributions, convolution, covariance, correlation<br><br>Thumbnail - <a href= http://img.youtube.com/vi/l4NoMKEHQwM/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec11_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-11-derived-distributions/id577778306?i=123745362>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/l4NoMKEHQwM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-11-derived-distributions-convolution-correlation Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Derived distributions convolution covariance correlation MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed conditional expectation and sum of a random number of random variables.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Iterated expectation, conditional expectation, means and variances<br><br>Thumbnail - <a href= http://img.youtube.com/vi/P7a4bjE6Crk/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec12_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-12-iterated-expectations/id577778306?i=123745427>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/P7a4bjE6Crk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-12-iterated-expectations-sum-of-a-random-number-of-random-variables Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Iterated expectation conditional expectation means and variances MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Bernoulli process, random processes, basic properties of Bernoulli process, distribution of interarrival times, the time of the kth success, merging and splitting.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Bernoulli process, random processes, merging, splitting<br><br>Thumbnail - <a href= http://img.youtube.com/vi/gMTiAeE0NCw/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec13_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-13-bernoulli-process/id577778306?i=123745411>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/gMTiAeE0NCw>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-13-bernoulli-process Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Bernoulli process random processes merging splitting MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Poisson process, Time homogeneity, Erlang distribution<br><br>Thumbnail - <a href= http://img.youtube.com/vi/jsqSScywvMc/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec14_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-14-poisson-process-i/id577778306?i=123745413>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/jsqSScywvMc>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-14-poisson-process-i Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Poisson process Time homogeneity Erlang distribution MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Poisson process, merging, splitting, and random incidence.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Poisson process, merging, splitting, random incidence<br><br>Thumbnail - <a href= http://img.youtube.com/vi/XsYXACeIklU/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec15_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-15-poisson-process-ii/id577778306?i=123745428>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/XsYXACeIklU>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-15-poisson-process-ii Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Poisson process merging splitting random incidence MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Markov process definition, n-step transition probabilities, and classification of states.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Markov process, finite state Markov chains, n-step transition probabilities, recurrent state, transient state<br><br>Thumbnail - <a href= http://img.youtube.com/vi/IkbkEtOOC1Y/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec16_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-16-markov-chains-i/id577778306?i=123745457>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/IkbkEtOOC1Y>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-16-markov-chains-i Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Markov process finite state Markov chains n-step transition probabilities recurrent state transient state MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Markov process, steady-state behavior, and birth-death processes.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Markov process, steady-state, recurrent state, transient state, periodic state<br><br>Thumbnail - <a href= http://img.youtube.com/vi/ZulMqrvP-Pk/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec17_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-17-markov-chains-ii/id577778306?i=123745453>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ZulMqrvP-Pk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-17-markov-chains-ii Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Markov process steady-state recurrent state transient state periodic state MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Markov Processes, probability of blocked phone calls, absorption probabilities, and calculating expected time to absorption.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Markov Processes, absorption probability, recurrent state, transient state<br><br>Thumbnail - <a href= http://img.youtube.com/vi/HIMxdWDLEK8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec18_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-18-markov-chains-iii/id577778306?i=123745455>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/HIMxdWDLEK8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-18-markov-chains-iii Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Markov Processes absorption probability recurrent state transient state MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed limit theorems, Chebyshev's inequality, and convergence &quot;in probability&quot;.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: limit theorems, Chebyshev's inequality, convergence<br><br>Thumbnail - <a href= http://img.youtube.com/vi/3eiio3Tw7UQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec19_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-19-weak-law-large/id577778306?i=123745452>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/3eiio3Tw7UQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-19-weak-law-of-large-numbers Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US limit theorems Chebyshev's inequality convergence MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed central limit theorem, Normal approximation, 1/2 correction for binomial approximation, and De Moivre&ndash;Laplace central limit theorem.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: central limit theorem, Normal approximation, binomial approximation, De Moivre–Laplace CLT<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Tx7zzD4aeiA/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec20_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-20-central-limit-theorem/id577778306?i=123745454>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Tx7zzD4aeiA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-20-the-central-limit-theorem Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US central limit theorem Normal approximation binomial approximation De Moivre–Laplace CLT MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Bayesian statistical inference and inference models.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p> <p><strong>Note:</strong> The first few minutes of this video are missing.</p>Keywords: Bayesian inference, Bayes rule, least mean square<br><br>Thumbnail - <a href= http://img.youtube.com/vi/1jDBM9UM9xk/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec21_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-21-bayesian-statistical/id577778306?i=123745450>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/1jDBM9UM9xk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-21-bayesian-statistical-inference-i Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Bayesian inference Bayes rule least mean square MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed Bayesian statistical inference, least means squares, and linear LMS estimation.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: Bayesian statistical inference, least means squares<br><br>Thumbnail - <a href= http://img.youtube.com/vi/XtNXQJkgkhI/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec22_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-22-bayesian-statistical/id577778306?i=123745456>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/XtNXQJkgkhI>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-22-bayesian-statistical-inference-ii Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US Bayesian statistical inference least means squares MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed classical statistics, maximum likelihood (ML) estimation, and confidence intervals.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: classical statistics, maximum likelihood, confidence interval<br><br>Thumbnail - <a href= http://img.youtube.com/vi/4UJc0S8APm4/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec23_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-23-classical-statistical/id577778306?i=123745458>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/4UJc0S8APm4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-23-classical-statistical-inference-i Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US classical statistics maximum likelihood confidence interval MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed classical inference, Linear regression, and binary hypothesis testing.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: classical inference, Linear regression, binary hypothesis<br><br>Thumbnail - <a href= http://img.youtube.com/vi/tBUHRpFZy0s/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec24_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-24-classical-inference/id577778306?i=123745429>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/tBUHRpFZy0s>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-24-classical-inference-ii Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US classical inference Linear regression binary hypothesis MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing.</p> <p><strong>Instructor:</strong> John Tsitsiklis</p>Keywords: classical inference, binary hypothesis, composite hypotheses<br><br>Thumbnail - <a href= http://img.youtube.com/vi/rYefUsYuEp0/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.041F10/MIT6_041F11_lec25_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-25-classical-inference/id577778306?i=123745451>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/rYefUsYuEp0>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-25-classical-inference-iii-course-overview Tsitsiklis, John 2011-03-10T07:04:12+05:00 en-US classical inference binary hypothesis composite hypotheses MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm