1
L01.1 Lecture Overview
1:52
2018-04-24
2
L01.2 Sample Space
5:38
2018-04-24
3
L01.3 Sample Space Examples
5:03
2018-04-24
4
L01.4 Probability Axioms
8:55
2018-04-24
5
L01.5 Simple Properties of Probabilities
11:05
2018-04-24
6
L01.6 More Properties of Probabilities
8:40
2018-04-24
7
L01.7 A Discrete Example
5:13
2018-04-24
8
L01.8 A Continuous Example
5:20
2018-04-24
9
L01.9 Countable Additivity
12:10
2018-04-24
10
L01.10 Interpretations & Uses of Probabilities
3:48
2018-04-24
11
S01.0 Mathematical Background Overview
1:25
2018-04-24
12
S01.1 Sets
10:55
2018-04-24
13
S01.2 De Morgan's Laws
4:53
2018-04-24
14
S01.3 Sequences and their Limits
6:00
2018-04-24
15
S01.4 When Does a Sequence Converge
2:46
2018-04-24
16
S01.5 Infinite Series
3:11
2018-04-24
17
S01.6 The Geometric Series
4:07
2018-04-24
18
S01.7 About the Order of Summation in Series with Multiple Indices
10:05
2018-04-24
19
S01.8 Countable and Uncountable Sets
6:19
2018-04-24
20
S01.9 Proof That a Set of Real Numbers is Uncountable
4:02
2018-04-24
21
S01.10 Bonferroni's Inequality
9:28
2018-04-24
22
L02.1 Lecture Overview
2:07
2018-04-24
23
L02.2 Conditional Probabilities
9:00
2018-04-24
24
L02.3 A Die Roll Example
5:02
2018-04-24
25
L02.4 Conditional Probabilities Obey the Same Axioms
7:45
2018-04-24
26
L02.5 A Radar Example and Three Basic Tools
10:59
2018-04-24
27
L02.6 The Multiplication Rule
6:17
2018-04-24
28
L02.7 Total Probability Theorem
5:25
2018-04-24
29
L02.8 Bayes' Rule
4:28
2018-04-24
30
L03.1 Lecture Overview
1:27
2018-04-24
31
L03.2 A Coin Tossing Example
7:59
2018-04-24
32
L03.3 Independence of Two Events
6:10
2018-04-24
33
L03.4 Independence of Event Complements
2:59
2018-04-24
34
L03.5 Conditional Independence
2:46
2018-04-24
35
L03.6 Independence Versus Conditional Independence
5:30
2018-04-24
36
L03.7 Independence of a Collection of Events
6:00
2018-04-24
37
L03.8 Independence Versus Pairwise Independence
8:35
2018-04-24
38
L03.9 Reliability
7:28
2018-04-24
39
L03.10 The King's Sibling
6:54
2018-04-24
40
L04.1 Lecture Overview
2:29
2018-04-24
41
L04.2 The Counting Principle
11:12
2018-04-24
42
L04.3 Die Roll Example
4:39
2018-04-24
43
L04.4 Combinations
10:08
2018-04-24
44
L04.5 Binomial Probabilities
6:38
2018-04-24
45
L04.6 A Coin Tossing Example
11:48
2018-04-24
46
L04.7 Partitions
5:20
2018-04-24
47
L04.8 Each Person Gets An Ace
9:45
2018-04-24
48
L04.9 Multinomial Probabilities
10:36
2018-04-24
49
L05.1 Lecture Overview
1:40
2018-04-24
50
L05.2 Definition of Random Variables
9:14
2018-04-24
51
L05.3 Probability Mass Functions
10:21
2018-04-24
52
L05.4 Bernoulli & Indicator Random Variables
3:06
2018-04-24
53
L05.5 Uniform Random Variables
4:06
2018-04-24
54
L05.6 Binomial Random Variables
6:08
2018-04-24
55
L05.7 Geometric Random Variables
7:37
2018-04-24
56
L05.8 Expectation
10:38
2018-04-24
57
L05.9 Elementary Properties of Expectation
4:12
2018-04-24
58
L05.10 The Expected Value Rule
10:00
2018-04-24
59
L05.11 Linearity of Expectations
3:59
2018-04-24
60
S05.1 Supplement: Functions
8:08
2018-04-24
61
L06.1 Lecture Overview
2:02
2018-04-24
62
L06.2 Variance
10:43
2018-04-24
63
L06.3 The Variance of the Bernoulli & The Uniform
8:40
2018-04-24
64
L06.4 Conditional PMFs & Expectations Given an Event
7:31
2018-04-24
65
L06.5 Total Expectation Theorem
6:28
2018-04-24
66
L06.6 Geometric PMF Memorylessness & Expectation
10:29
2018-04-24
67
L06.7 Joint PMFs and the Expected Value Rule
10:16
2018-04-24
68
L06.8 Linearity of Expectations & The Mean of the Binomial
8:25
2018-04-24
69
L07.1 Lecture Overview
1:50
2018-04-24
70
L07.2 Conditional PMFs
10:48
2018-04-24
71
L07.3 Conditional Expectation & the Total Expectation Theorem
6:10
2018-04-24
72
L07.4 Independence of Random Variables
5:08
2018-04-24
73
L07.5 Example
4:44
2018-04-24
74
L07.6 Independence & Expectations
4:22
2018-04-24
75
L07.7 Independence, Variances & the Binomial Variance
7:09
2018-04-24
76
L07.8 The Hat Problem
16:09
2018-04-24
77
S07.1 The Inclusion-Exclusion Formula
11:13
2018-04-24
78
S07.2 The Variance of the Geometric
5:42
2018-04-24
79
S07.3 Independence of Random Variables Versus Independence of Events
6:51
2018-04-24
80
L08.1 Lecture Overview
1:13
2018-04-24
81
L08.2 Probability Density Functions
11:09
2018-04-24
82
L08.3 Uniform & Piecewise Constant PDFs
2:52
2018-04-24
83
L08.4 Means & Variances
6:57
2018-04-24
84
L08.5 Mean & Variance of the Uniform
3:56
2018-04-24
85
L08.6 Exponential Random Variables
8:09
2018-04-24
86
L08.7 Cumulative Distribution Functions
12:48
2018-04-24
87
L08.8 Normal Random Variables
9:14
2018-04-24
88
L08.9 Calculation of Normal Probabilities
10:11
2018-04-24
89
L09.1 Lecture Overview
1:33
2018-04-24
90
L09.2 Conditioning A Continuous Random Variable on an Event
9:56
2018-04-24
91
L09.3 Conditioning Example
3:08
2018-04-24
92
L09.4 Memorylessness of the Exponential PDF
8:18
2018-04-24
93
L09.5 Total Probability & Expectation Theorems
6:51
2018-04-24
94
L09.6 Mixed Random Variables
5:35
2018-04-24
95
L09.7 Joint PDFs
9:18
2018-04-24
96
L09.8 From The Joint to the Marginal
7:23
2018-04-24
97
L09.9 Continuous Analogs of Various Properties
1:40
2018-04-24
98
L09.10 Joint CDFs
4:16
2018-04-24
99
S09.1 Buffon's Needle & Monte Carlo Simulation
16:12
2018-04-24
100
L10.1 Lecture Overview
1:42
2018-04-24
101
L10.2 Conditional PDFs
6:57
2018-04-24
102
L10.3 Comments on Conditional PDFs
4:34
2018-04-24
103
L10.4 Total Probability & Total Expectation Theorems
5:17
2018-04-24
104
L10.5 Independence
3:35
2018-04-24
105
L10.6 Stick-Breaking Example
10:02
2018-04-24
106
L10.7 Independent Normals
5:36
2018-04-24
107
L10.8 Bayes Rule Variations
3:27
2018-04-24
108
L10.9 Mixed Bayes Rule
8:33
2018-04-24
109
L10.10 Detection of a Binary Signal
9:15
2018-04-24
110
L10.11 Inference of the Bias of a Coin
6:00
2018-04-24
111
L11.1 Lecture Overview
1:52
2018-04-24
112
L11.2 The PMF of a Function of a Discrete Random Variable
6:42
2018-04-24
113
L11.3 A Linear Function of a Continuous Random Variable
11:18
2018-04-24
114
L11.4 A Linear Function of a Normal Random Variable
2:45
2018-04-24
115
L11.5 The PDF of a General Function
9:47
2018-04-24
116
L11.6 The Monotonic Case
11:07
2018-04-24
117
L11.7 The Intuition for the Monotonic Case
5:28
2018-04-24
118
L11.8 A Nonmonotonic Example
7:14
2018-04-24
119
L11.9 The PDF of a Function of Multiple Random Variables
7:42
2018-04-24
120
S11.1 Simulation
12:35
2018-04-24
121
L12.1 Lecture Overview
1:29
2018-04-24
122
L12.2 The Sum of Independent Discrete Random Variables
7:52
2018-04-24
123
L12.3 The Sum of Independent Continuous Random Variables
6:45
2018-04-24
124
L12.4 The Sum of Independent Normal Random Variables
3:10
2018-04-24
125
L12.5 Covariance
5:54
2018-04-24
126
L12.6 Covariance Properties
5:48
2018-04-24
127
L12.7 The Variance of the Sum of Random Variables
5:36
2018-04-24
128
L12.8 The Correlation Coefficient
7:03
2018-04-24
129
L12.9 Proof of Key Properties of the Correlation Coefficient
3:52
2018-04-24
130
L12.10 Interpreting the Correlation Coefficient
5:50
2018-04-24
131
L12.11 Correlations Matter
6:22
2018-04-24
132
L13.1 Lecture Overview
1:47
2018-04-24
133
L13.2 Conditional Expectation as a Random Variable
4:31
2018-04-24
134
L13.3 The Law of Iterated Expectations
3:58
2018-04-24
135
L13.4 Stick-Breaking Revisited
3:53
2018-04-24
136
L13.5 Forecast Revisions
4:38
2018-04-24
137
L13.6 The Conditional Variance
5:02
2018-04-24
138
L13.7 Derivation of the Law of Total Variance
4:54
2018-04-24
139
L13.8 A Simple Example
6:29
2018-04-24
140
L13.9 Section Means and Variances
9:04
2018-04-24
141
L13.10 Mean of the Sum of a Random Number of Random Variables
6:26
2018-04-24
142
L13.11 Variance of the Sum of a Random Number of Random Variables
5:10
2018-04-24
143
S13.1 Conditional Expectation Properties
8:13
2018-04-24
144
L14.1 Lecture Overview
2:10
2018-04-24
145
L14.2 Overview of Some Application Domains
5:17
2018-04-24
146
L14.3 Types of Inference Problems
5:24
2018-04-24
147
L14.4 The Bayesian Inference Framework
9:48
2018-04-24
148
L14.5 Discrete Parameter, Discrete Observation
6:46
2018-04-24
149
L14.6 Discrete Parameter, Continuous Observation
4:35
2018-04-24
150
L14.7 Continuous Parameter, Continuous Observation
3:46
2018-04-24
151
L14.8 Inferring the Unknown Bias of a Coin and the Beta Distribution
7:35
2018-04-24
152
L14.9 Inferring the Unknown Bias of a Coin - Point Estimates
9:30
2018-04-24
153
L14.10 Summary
5:41
2018-04-24
154
S14.1 The Beta Formula
10:24
2018-04-24
155
L15.1 Lecture Overview
1:59
2018-04-24
156
L15.2 Recognizing Normal PDFs
7:15
2018-04-24
157
L15.3 Estimating a Normal Random Variable in the Presence of Additive Noise
8:18
2018-04-24
158
L15.4 The Case of Multiple Observations
13:47
2018-04-24
159
L15.5 The Mean Squared Error
13:02
2018-04-24
160
L15.6 Multiple Parameters; Trajectory Estimation
10:32
2018-04-24
161
L15.7 Linear Normal Models
5:12
2018-04-24
162
L15.8 Trajectory Estimation Illustration
10:55
2018-04-24
163
L16.1 Lecture Overview
1:13
2018-04-24
164
L16.2 LMS Estimation in the Absence of Observations
6:48
2018-04-24
165
L16.3 LMS Estimation of One Random Variable Based on Another
9:24
2018-04-24
166
L16.4 LMS Performance Evaluation
4:32
2018-04-24
167
L16.5 Example: The LMS Estimate
6:31
2018-04-24
168
L16.6 Example Continued: LMS Performance Evaluation
5:29
2018-04-24
169
L16.7 LMS Estimation with Multiple Observations or Unknowns
5:24
2018-04-24
170
L16.8 Properties of the LMS Estimation Error
5:59
2018-04-24
171
L17.1 Lecture Overview
1:41
2018-04-24
172
L17.2 LLMS Formulation
4:58
2018-04-24
173
L17.3 Solution to the LLMS Problem
5:06
2018-04-24
174
L17.4 Remarks on the LLMS Solution and on the Error Variance
8:02
2018-04-24
175
L17.5 LLMS Example
6:43
2018-04-24
176
L17.6 LLMS for Inferring the Parameter of a Coin
11:29
2018-04-24
177
L17.7 LLMS with Multiple Observations
6:54
2018-04-24
178
L17.8 The Simplest LLMS Example with Multiple Observations
5:06
2018-04-24
179
L17.9 The Representation of the Data Matters in LLMS
7:03
2018-04-24
180
L18.1 Lecture Overview
1:57
2018-04-24
181
L18.2 The Markov Inequality
10:21
2018-04-24
182
L18.3 The Chebyshev Inequality
5:57
2018-04-24
183
L18.4 The Weak Law of Large Numbers
7:31
2018-04-24
184
L18.5 Polling
8:12
2018-04-24
185
L18.6 Convergence in Probability
8:28
2018-04-24
186
L18.7 Convergence in Probability Examples
8:05
2018-04-24
187
L18.8 Related Topics
6:44
2018-04-24
188
S18.1 Convergence in Probability of the Sum of Two Random Variables
10:13
2018-04-24
189
S18.2 Jensen's Inequality
12:19
2018-04-24
190
S18.3 Hoeffding's Inequality
18:28
2018-04-24
191
L19.1 Lecture Overview
1:50
2018-04-24
192
L19.2 The Central Limit Theorem
6:58
2018-04-24
193
L19.3 Discussion of the CLT
9:00
2018-04-24
194
L19.4 Illustration of the CLT
2:54
2018-04-24
195
L19.5 CLT Examples
13:56
2018-04-24
196
L19.6 Normal Approximation to the Binomial
11:53
2018-04-24
197
L19.7 Polling Revisited
13:54
2018-04-24
198
L20.1 Lecture Overview
2:46
2018-04-24
199
L20.2 Overview of the Classical Statistical Framework
11:00
2018-04-24
200
L20.3 The Sample Mean and Some Terminology
4:58
2018-04-24
201
L20.4 On the Mean Squared Error of an Estimator
6:53
2018-04-24
202
L20.5 Confidence Intervals
5:04
2018-04-24
203
L20.6 Confidence Intervals for the Estimation of the Mean
4:27
2018-04-24
204
L20.7 Confidence Intervals for the Mean, When the Variance is Unknown
6:13
2018-04-24
205
L20.8 Other Natural Estimators
4:37
2018-04-24
206
L20.9 Maximum Likelihood Estimation
6:32
2018-04-24
207
L20.10 Maximum Likelihood Estimation Examples
10:20
2018-04-24
208
L21.1 Lecture Overview
2:01
2018-04-24
209
L21.2 The Bernoulli Process
4:21
2018-04-24
210
L21.3 Stochastic Processes
6:21
2018-04-24
211
L21.4 Review of Known Properties of the Bernoulli Process
2:20
2018-04-24
212
L21.5 The Fresh Start Property
11:26
2018-04-24
213
L21.6 Example: The Distribution of a Busy Period
4:16
2018-04-24
214
L21.7 The Time of the K-th Arrival
8:12
2018-04-24
215
L21.8 Merging of Bernoulli Processes
7:12
2018-04-24
216
L21.9 Splitting a Bernoulli Process
5:54
2018-04-24
217
L21.10 The Poisson Approximation to the Binomial
6:12
2018-04-24
218
L22.1 Lecture Overview
1:31
2018-04-24
219
L22.2 Definition of the Poisson Process
5:07
2018-04-24
220
L22.3 Applications of the Poisson Process
3:03
2018-04-24
221
L22.4 The Poisson PMF for the Number of Arrivals
8:01
2018-04-24
222
L22.5 The Mean and Variance of the Number of Arrivals
3:22
2018-04-24
223
L22.6 A Simple Example
3:07
2018-04-24
224
L22.7 Time of the K-th Arrival
10:41
2018-04-24
225
L22.8 The Fresh Start Property and Its Implications
10:33
2018-04-24
226
L22.9 Summary of Results
2:34
2018-04-24
227
L22.10 An Example
14:08
2018-04-24
228
L23.1 Lecture Overview
1:39
2018-04-24
229
L23.2 The Sum of Independent Poisson Random Variables
4:03
2018-04-24
230
L23.3 Merging Independent Poisson Processes
8:22
2018-04-24
231
L23.4 Where is an Arrival of the Merged Process Coming From?
5:00
2018-04-24
232
L23.5 The Time Until the First (or last) Lightbulb Burns Out
11:25
2018-04-24
233
L23.6 Splitting a Poisson Process
5:06
2018-04-24
234
L23.7 Random Incidence in the Poisson Process
9:09
2018-04-24
235
L23.8 Random Incidence in a Non-Poisson Process
4:36
2018-04-24
236
L23.9 Different Sampling Methods can Give Different Results
3:59
2018-04-24
237
S23.1 Poisson Versus Normal Approximations to the Binomial
8:56
2018-04-24
238
S23.2 Poisson Arrivals During an Exponential Interval
9:37
2018-04-24
239
L24.1 Lecture Overview
1:59
2018-04-24
240
L24.2 Introduction to Markov Processes
2:09
2018-04-24
241
L24.3 Checkout Counter Example
12:10
2018-04-24
242
L24.4 Discrete-Time Finite-State Markov Chains
7:53
2018-04-24
243
L24.5 N-Step Transition Probabilities
10:59
2018-04-24
244
L24.6 A Numerical Example - Part I
9:26
2018-04-24
245
L24.7 Generic Convergence Questions
5:32
2018-04-24
246
L24.8 Recurrent and Transient States
5:37
2018-04-24
247
L25.1 Brief Introduction (RES.6-012 Introduction to Probability)
1:40
2018-04-24
248
L25.2 Lecture Overview
1:05
2018-04-24
249
L25.3 Markov Chain Review
6:15
2018-04-24
250
L25.4 The Probability of a Path
6:39
2018-04-24
251
L25.5 Recurrent and Transient States: Review
3:26
2018-04-24
252
L25.6 Periodic States
6:49
2018-04-24
253
L25.7 Steady-State Probabilities and Convergence
9:13
2018-04-24
254
L25.8 A Numerical Example - Part II
3:58
2018-04-24
255
L25.9 Visit Frequency Interpretation of Steady-State Probabilities
5:19
2018-04-24
256
L25.10 Birth-Death Processes - Part I
8:56
2018-04-24
257
L25.11 Birth-Death Processes - Part II
8:57
2018-04-24
258
L26.1 Brief Introduction (RES.6-012 Introduction to Probability)
1:41
2018-04-24
259
L26.2 Lecture Overview
0:40
2018-04-24
260
L26.3 Review of Steady-State Behavior
9:12
2018-04-24
261
L26.4 A Numerical Example - Part III
10:35
2018-04-24
262
L26.5 Design of a Phone System
18:30
2018-04-24
263
L26.6 Absorption Probabilities
9:58
2018-04-24
264
L26.7 Expected Time to Absorption
11:30
2018-04-24
265
L26.8 Mean First Passage Time
8:44
2018-04-24
266
L26.9 Gambler's Ruin
11:24
2018-04-24
