Probability Foundation for Electrical Engineers by Krishna Jagannathan (IIT Madras)

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source: nptelhrd    2015年2月19日
Electrical - Probability Foundation for Electrical Engineers by Dr. Krishna Jagannathan, Department of Electrical Engineering, IIT Madras. For more details on NPTEL visit http://nptel.ac.in

01 INTRODUCTION 34:55
02 CARDINALITY AND COUNTABILITY-1 41:53
03 CARDINALITY AND COUNTABILITY-2 39:34
04 PROBABILITY SPACES-1 52:11
05 PROBABILITY SPACES-2 51:30
06 PROPERTIES OF PROBABILITY MEASURES 50:06
07 DISCRETE PROBABILITY SPACES 45:40
08 GENERATED Σ-ALGEBRA, BOREL SETS 27:19
09 BOREL SETS AND LEBESGUE MEASURE-1 50:11
10 BOREL SETS AND LEBESGUE MEASURE-2 50:27
11 THE INFINITE COIN TOSS MODEL 49:24
12 CONDITIONAL PROBABILITY AND INDEPENDENCE 50:22
13 INDEPENDENCE CONTD. 41:05
14 THE BOREL-CANTELLI LEMMAS 51:11
15 RANDOM VARIABLES 47:41
16 CUMULATIVE DISTRIBUTION FUNCTION 46:16
17 TYPES OF RANDOM VARIABLES 45:17
18 CONTINUOUS RANDOM VARIABLES 44:33
19 CONTINUOUS RANDOM VARIABLES (CONTD.) AND SINGULAR RANDOM VARIABLES 47:20
20 SEVERAL RANDOM VARIABLES 49:29
21 INDEPENDENT RANDOM VARIABLES-1 46:10
23 JOINTLY CONTINUOUS RANDOM VARIABLES 46:09
24 TRANSFORMATION OF RANDOM VARIABLES-1 52:14
25 TRANSFORMATION OF RANDOM VARIABLES-2 46:45
26 TRANSFORMATION OF RANDOM VARIABLES-3 44:38
27 TRANSFORMATION OF RANDOM VARIABLES-4 48:20
28 INTEGRATION AND EXPECTATION-1 50:21
29 INTEGRATION AND EXPECTATION-2 43:05
30 PROPERTIES OF INTEGRALS 50:28
31 MONOTONE CONVERGENCE THEOREM 47:26
32 EXPECTATION OF DICRETE RANDOM VARIABLES, EXPECTATION OVER DIFFERENT SPACES 47:29
33 EXPECTATION OF DICRETE RANDOM VARIABLES 46:17
34 FATOU’S LEMMA & DOMINATED CONVERGENCE THEOREM 42:09
35 VARIANCE AND COVARIANCE 49:01
36 COVARIANCE, CORRELATION COEFFICIENT 42:56
37 CONDITIONAL EXPECTATION 53:28
38 MMSE ESTIMATOR, TRANSFORMS 44:54
39 MOMENT GENERATING FUNCTION 50:22
40 CHARACTERISTIC FUNCTION – 1 49:21
41 CHARACTERISTIC FUNCTION – 2 43:39
42 CONCENTRATION INEQUALITIES 47:00
43 CONVERGENCE OF RANDOM VARIABLES – 1 43:49
44 CONVERGENCE OF RANDOM VARIABLES – 2 50:37
45 CONVERGENCE OF RANDOM VARIABLES – 3 45:51
46 CONVERGENCE OF CHARACTERISTIC FUNCTIONS, LIMIT THEOREMS 45:18
47 THE LAWS OF LARGE NUMBERS 49:07
48 THE CENTRAL LIMIT THEOREM 43:29
49 A BRIEF OVERVIEW OF MULTIVARIATE GAUSSIANS 58:54