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EE 531 - Probability and Stochastic Processes
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EE 531
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Lecture 1: MEASURABLE SPACES
Lecture 1: MEASURABLE SPACES
Lecture 1: MEASURABLE SPACES
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Lecture 2: PROBABILITY SPACES
Lecture 3: CONTINUITY OF PROBABILITY, BAYES' S RULE, INDEPENDENCE
Lecture 4: BOREL CANTELLI LEMMAS
Lecture 5: PROOF OF THE BOREL CANTELLI LEMMAS
Lecture 6: RANDOM VARIABLES
Lecture 7: CUMULATIVE DISTRIBUTION FUNCTION (CDF)
Lecture 8: DISCRETE RANDOM VARIABLES
Lecture 9: CONTINUOUS RANDOM VARIABLES
Lecture 10: INTRODUCTION TO STOCHASTIC PROCESSES
Lecture 11: DISCRETE STOCHASTIC PROCESSES
Lecture 12: EXPECTATION
Lecture 13: VARIANCE
Lecture 14: COVARIANCE
Lecture 15: CONDITIONAL EXPECTATION
Lecture 16: ITERATED EXPECTATION
Lecture 17: MARKOV & CHEBYCHEV INEQUALITIES
Lecture 18: CONVERGENCE IN PROBABILITY
Lecture 19: CONVERGENCE IN DISTRIBUTION
Lecture 20: MEAN SQUARE SENSE AND ALMOST SURE CONVERGENCE
Lecture 21: EXAMPLE: ALMOST SURE CONVERGENCE
Lecture 22: EXAMPLE: IN PROBABILITY vs MSE CONVERGENCE
Lecture 23: EXAMPLE: MSE CONVERGENCE DOES NOT IMPLY ALMOST SURE CONVERGENCE
Lecture 24: COUNTING PROCESSES
Lecture 25: THE POISSON PROCESS (DEFINITION 1)
Lecture 26: THE POISSON PROCESS (DEFINITION 2)
Lecture 27: THE POISSON PROCESS (DEFINITION 3)
Lecture 28: MERGING AND SPLITTING POISSON PROCESSES
Lecture 29: POISSON PROCESS EXAMPLE
Lecture 30- MARKOV CHAINS
Lecture 31: CONVERGENCE IN MARKOV CHAINS
Lecture 32: MARKOV CHAINS: CLASSIFICATION OF STATES PART 1
Lecture 33: MARKOV CHAINS: CLASSIFICATION OF STATES PART 2
Lecture 34: CLASSIFICATION OF MARKOV CHAINS
Lecture 35: MARKOV CHAINS: CONVERGENCE
Lecture 36: STATIONARY DISTRIBUTIONS IN A MARKOV CHAIN
Lecture 37: EXPECTED FIRST PASSAGE TIME
Lecture 38: MARKOV CHAINS WITH REWARDS
Lecture 39: STRONG LAW FOR RENEWAL PROCESSES
Lecture 40: RENEWAL REWARD PROCESSES TIME AVERAGE REWARD
Lecture 41: EXAMPLES RENEWAL REWARD PROCESSES TIME AVERAGE REWARD
Lecture 42: MARTINGALES
Lecture 43: MARTINGALES - 2
Lecture 44: STOPPING TIMES
Lecture 45: STOPPED MARTINGALES AND WALD'S EQUALITY
Lecture 46: APPLICATION OF WALD'S EQUALITY
Lecture 2: PROBABILITY SPACES ►
EE 531
Course Materials
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