MIT RES.6-012 Introduction to Probability, Spring 2018麻省理工：概率学导论，2018春季-L25.4 The Probability of a PathL25.4路径的概率-网易公开课

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L25.4 The Probability of a PathL25.4路径的概率

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[1] L01.1 Lecture Ove...

1.8万播放

01:51

L01.1 Lecture Overviewl01.1讲座概述

[2] L01.2 Sample Spac...

5767播放

05:37

L01.2 Sample SpaceL01.2样本空间

[3] L01.3 Sample Spac...

3701播放

05:02

L01.3 Sample Space ExamplesL01.3示例空间示例

[4] L01.4 Probability...

2522播放

08:54

L01.4 Probability AxiomsL01.4概率公理

[5] L01.5 Simple Prop...

1768播放

11:04

L01.5 Simple Properties of Probabilitiesl01.5概率的简单属性

[6] L01.6 More Proper...

1737播放

08:39

L01.6 More Properties of Probabilitiesl01.6更多概率的属性

[7] L01.7 A Discrete ...

2046播放

05:12

L01.7 A Discrete Examplel01.7一个离散的例子

[8] L01.8 A Continuou...

1466播放

05:19

L01.8 A Continuous Examplel01.8一个连续的例子

[9] L01.9 Countable A...

1198播放

12:09

L01.9 Countable AdditivityL01.9可数添加性

[10] L01.10 Interpreta...

1950播放

03:47

L01.10 Interpretations & Uses of Probabilitiesl01.10概率的解释和用途

[11] S01.0 Mathematica...

1440播放

01:24

S01.0 Mathematical Background OverviewS01.0数学背景概述

[12] S01.1 SetsS01.1套装

1423播放

10:54

S01.1 SetsS01.1套装

[13] S01.2 De Morgan's...

1990播放

04:52

S01.2 De Morgan's LawsS01.2 DEM organs laws

[14] S01.3 Sequences a...

1137播放

05:59

S01.3 Sequences and their LimitsS01.3序列及其限制

[15] S01.4 When Does a...

1686播放

02:45

S01.4 When Does a Sequence ConvergeS01.4序列何时会聚

[16] S01.5 Infinite Se...

1477播放

03:10

S01.5 Infinite SeriesS01.5无限系列

[17] S01.6 The Geometr...

1703播放

04:06

S01.6 The Geometric SeriesS01.6几何系列

[18] S01.7 About the O...

1814播放

10:04

S01.7 About the Order of Summation in Series with Multiple IndicesS01.7关于串联序列的序列与多个指标

[19] S01.8 Countable a...

1658播放

06:18

S01.8 Countable and Uncountable SetsS01.8可数和不可数集合

[20] S01.9 Proof That ...

1235播放

04:01

S01.9 Proof That a Set of Real Numbers is UncountableS01.9证明一组实数是不可数的

[21] S01.10 Bonferroni...

1048播放

09:27

S01.10 Bonferroni's InequalityS01.10 Bonferroni的不平等

[22] L02.1 Lecture Ove...

1959播放

02:06

L02.1 Lecture OverviewL02.1讲座概述

[23] L02.2 Conditional...

2156播放

08:59

L02.2 Conditional Probabilitiesl02.2条件概率

[24] L02.3 A Die Roll ...

1012播放

05:01

L02.3 A Die Roll ExampleL02.3 DIS滚动示例

[25] L02.4 Conditional...

1895播放

07:44

L02.4 Conditional Probabilities Obey the Same AxiomsL02.4条件概率遵守相同的公理

[26] L02.5 A Radar Exa...

1222播放

10:58

L02.5 A Radar Example and Three Basic Toolsl02.5雷达例和三个基本工具

[27] L02.6 The Multipl...

1109播放

06:16

L02.6 The Multiplication Rulel02.6乘法规则

[28] L02.7 Total Proba...

1710播放

05:24

L02.7 Total Probability TheoremL02.7总概率定理

[29] L02.8 Bayes' Rule...

2076播放

04:27

L02.8 Bayes' RuleL02.8贝叶斯的规则

[30] L03.1 Lecture Ove...

1308播放

01:26

L03.1 Lecture Overviewl03.1讲座概述

[31] L03.2 A Coin Toss...

1397播放

07:59

L03.2 A Coin Tossing Examplel03.2硬币折腾举例

[32] L03.3 Independenc...

1091播放

06:09

L03.3 Independence of Two Eventsl03.3两个事件的独立性

[34] L03.5 Conditional...

2054播放

02:45

L03.5 Conditional IndependenceL03.5条件独立性

[35] L03.6 Independenc...

1720播放

05:29

L03.6 Independence Versus Conditional Independencel03.6独立与条件独立性

[36] L03.7 Independenc...

1713播放

05:59

L03.7 Independence of a Collection of Eventsl03.7事件集合的独立性

[37] L03.8 Independenc...

1277播放

08:34

L03.8 Independence Versus Pairwise Independencel03.8独立与成对独立性

[38] L03.9 Reliability...

2964播放

07:27

L03.9 Reliabilityl03.9可靠性

[39] L03.10 The King's...

1189播放

06:53

L03.10 The King's Siblingl03.10国王的兄弟姐妹

[40] L04.1 Lecture Ove...

1911播放

02:28

L04.1 Lecture OverviewL04.1讲座概述

[41] L04.2 The Countin...

1585播放

11:11

L04.2 The Counting Principlel04.2计数原则

[42] L04.3 Die Roll Ex...

1472播放

04:38

L04.3 Die Roll ExampleL04.3管芯滚动示例

[43] L04.4 Combination...

1791播放

10:07

L04.4 CombinationsL04.4组合

[44] L04.5 Binomial Pr...

1816播放

06:37

L04.5 Binomial Probabilitiesl04.5二项概率

[45] L04.6 A Coin Toss...

1584播放

11:48

L04.6 A Coin Tossing Examplel04.6硬币折腾举例

[46] L04.7 Partitionsl...

1733播放

05:19

L04.7 Partitionsl04.7分区

[47] L04.8 Each Person...

1750播放

09:44

L04.8 Each Person Gets An Acel04.8每个人都得到一个王牌

[48] L04.9 Multinomial...

1400播放

10:35

L04.9 Multinomial ProbabilitiesL04.9多项概率

[49] L05.1 Lecture Ove...

1457播放

01:39

L05.1 Lecture OverviewL05.1讲座概述

[50] L05.2 Definition ...

1804播放

09:13

L05.2 Definition of Random Variablesl05.2随机变量的定义

[51] L05.3 Probability...

1681播放

10:20

L05.3 Probability Mass FunctionsL05.3概率质量功能

[52] L05.4 Bernoulli &...

1003播放

03:05

L05.4 Bernoulli & Indicator Random VariablesL05.4 Bernoulli和指示器随机变量

[53] L05.5 Uniform Ran...

1404播放

04:05

L05.5 Uniform Random Variablesl05.5均匀随机变量

[54] L05.6 Binomial Ra...

1214播放

06:07

L05.6 Binomial Random Variablesl05.6二项式随机变量

[55] L05.7 Geometric R...

1644播放

07:36

L05.7 Geometric Random Variablesl05.7几何随机变量

[56] L05.8 Expectation...

968播放

10:37

L05.8 Expectationl05.8期望

[57] L05.9 Elementary ...

1492播放

04:11

L05.9 Elementary Properties of ExpectationL05.9期望的基本属性

[58] L05.10 The Expect...

1342播放

09:59

L05.10 The Expected Value RuleL05.10预期值规则

[59] L05.11 Linearity ...

1151播放

03:58

L05.11 Linearity of Expectationsl05.11期望的线性

[60] S05.1 Supplement:...

1170播放

08:07

S05.1 Supplement: FunctionsS05.1补充：功能

[61] L06.1 Lecture Ove...

993播放

02:01

L06.1 Lecture OverviewL06.1讲座概述

[62] L06.2 Variancel06...

794播放

10:42

L06.2 Variancel06.2方差

[63] L06.3 The Varianc...

800播放

08:39

L06.3 The Variance of the Bernoulli & The Uniforml06.3伯努利和制服的方差

[64] L06.4 Conditional...

1043播放

07:30

L06.4 Conditional PMFs & Expectations Given an EventL06.4条件PMF和期望给出了一个事件

[65] L06.5 Total Expec...

1183播放

06:27

L06.5 Total Expectation TheoremL06.5总期望定理

[66] L06.6 Geometric P...

1395播放

10:28

L06.6 Geometric PMF Memorylessness & ExpectationL06.6几何PMF记忆和期望

[67] L06.7 Joint PMFs ...

1292播放

10:15

L06.7 Joint PMFs and the Expected Value RuleL06.7联合PMF和预期价值规则

[68] L06.8 Linearity o...

911播放

08:25

L06.8 Linearity of Expectations & The Mean of the Binomiall06.8期望的线性和二项式的平均值

[69] L07.1 Lecture Ove...

1273播放

01:49

L07.1 Lecture OverviewL07.1讲座概述

[70] L07.2 Conditional...

1057播放

10:47

L07.2 Conditional PMFsL07.2条件PMFS

[71] L07.3 Conditional...

1643播放

06:09

L07.3 Conditional Expectation & the Total Expectation TheoremL07.3条件期望和总期望定理

[72] L07.4 Independenc...

1175播放

05:08

L07.4 Independence of Random Variablesl07.4随机变量的独立性

[73] L07.5 Examplel07....

1324播放

04:43

L07.5 Examplel07.5示例

[74] L07.6 Independenc...

863播放

04:21

L07.6 Independence & ExpectationsL07.6独立和期望

[75] L07.7 Independenc...

1492播放

07:08

L07.7 Independence, Variances & the Binomial Variancel07.7独立性，差异和二项式方差

[76] L07.8 The Hat Pro...

1540播放

16:08

L07.8 The Hat Probleml07.8帽子问题

[77] S07.1 The Inclusi...

1550播放

11:12

S07.1 The Inclusion-Exclusion FormulaS07.1包含排除公式

[78] S07.2 The Varianc...

766播放

05:41

S07.2 The Variance of the GeometricS07.2几何方差

[79] S07.3 Independenc...

743播放

06:50

S07.3 Independence of Random Variables Versus Independence of EventsS07.3随机变量的独立性与事件的独立性

[80] L08.1 Lecture Ove...

1376播放

01:12

L08.1 Lecture OverviewL08.1讲座概述

[81] L08.2 Probability...

1752播放

11:08

L08.2 Probability Density FunctionsL08.2概率密度函数

[82] L08.3 Uniform & P...

1034播放

02:51

L08.3 Uniform & Piecewise Constant PDFsL08.3统一和分段常量PDF

[83] L08.4 Means & Var...

1545播放

06:56

L08.4 Means & Variancesl08.4手段和差异

[84] L08.5 Mean & Vari...

1244播放

03:55

L08.5 Mean & Variance of the Uniforml08.5制服的平均值和方差

[85] L08.6 Exponential...

1573播放

08:08

L08.6 Exponential Random Variablesl08.6指数随机变量

[86] L08.7 Cumulative ...

1351播放

12:47

L08.7 Cumulative Distribution FunctionsL08.7累积分配功能

[87] L08.8 Normal Rand...

921播放

09:13

L08.8 Normal Random Variablesl08.8正常随机变量

[88] L08.9 Calculation...

691播放

10:10

L08.9 Calculation of Normal ProbabilitiesL08.9正常概率的计算

[89] L09.1 Lecture Ove...

973播放

01:32

L09.1 Lecture OverviewL09.1讲座概述

[90] L09.2 Conditionin...

1193播放

09:55

L09.2 Conditioning A Continuous Random Variable on an Eventl09.2在事件上调节连续随机变量

[91] L09.3 Conditionin...

1524播放

03:07

L09.3 Conditioning ExampleL09.3条件示例

[92] L09.4 Memorylessn...

1583播放

08:17

L09.4 Memorylessness of the Exponential PDFL09.4指数PDF的内核

[93] L09.5 Total Proba...

1547播放

06:50

L09.5 Total Probability & Expectation TheoremsL09.5总概率和期望定理

[94] L09.6 Mixed Rando...

1020播放

05:34

L09.6 Mixed Random Variablesl09.6混合随机变量

[95] L09.7 Joint PDFsL...

1147播放

09:17

L09.7 Joint PDFsL09.7联合PDF

[96] L09.8 From The Jo...

865播放

07:22

L09.8 From The Joint to the MarginalL09.8从关节到边缘

[97] L09.9 Continuous ...

744播放

01:39

L09.9 Continuous Analogs of Various PropertiesL09.9各种性能的连续类似物

[98] L09.10 Joint CDFs...

654播放

04:15

L09.10 Joint CDFsL09.10联合CDF

[99] S09.1 Buffon's Ne...

1436播放

16:11

S09.1 Buffon's Needle & Monte Carlo SimulationS09.1缓冲器的针头和蒙特卡罗模拟

[100] L10.1 Lecture Ove...

977播放

01:41

L10.1 Lecture OverviewL10.1讲座概述

[101] L10.2 Conditional...

691播放

06:56

L10.2 Conditional PDFsL10.2条件PDF

[102] L10.3 Comments on...

1386播放

04:33

L10.3 Comments on Conditional PDFsL10.3条件PDF的评论

[103] L10.4 Total Proba...

1748播放

05:16

L10.4 Total Probability & Total Expectation TheoremsL10.4总概率和总期望定理

[104] L10.5 Independenc...

1520播放

03:34

L10.5 IndependenceL10.5独立性

[105] L10.6 Stick-Break...

782播放

10:01

L10.6 Stick-Breaking Examplel10.6粘性例子

[106] L10.7 Independent...

1510播放

05:35

L10.7 Independent NormalsL10.7独立的法线

[107] L10.8 Bayes Rule ...

1412播放

03:26

L10.8 Bayes Rule VariationsL10.8贝叶斯规则变化

[108] L10.9 Mixed Bayes...

811播放

08:32

L10.9 Mixed Bayes RuleL10.9混合贝叶斯规则

[109] L10.10 Detection ...

1031播放

09:14

L10.10 Detection of a Binary SignalL10.10检测二进制信号

[110] L10.11 Inference ...

1329播放

05:59

L10.11 Inference of the Bias of a Coinl10.11硬币偏差的推理

[111] L11.1 Lecture Ove...

1193播放

01:51

L11.1 Lecture OverviewL11.1讲座概述

[112] L11.2 The PMF of ...

602播放

06:41

L11.2 The PMF of a Function of a Discrete Random VariableL11.2离散随机变量的函数的PMF

[113] L11.3 A Linear Fu...

1217播放

11:17

L11.3 A Linear Function of a Continuous Random Variablel11.3连续随机变量的线性函数

[114] L11.4 A Linear Fu...

725播放

02:44

L11.4 A Linear Function of a Normal Random Variablel11.4正常随机变量的线性函数

[115] L11.5 The PDF of ...

639播放

09:47

L11.5 The PDF of a General Functionl11.5通用功能的PDF

[116] L11.6 The Monoton...

1253播放

11:06

L11.6 The Monotonic Casel11.6单调案例

[117] L11.7 The Intuiti...

1139播放

05:27

L11.7 The Intuition for the Monotonic Casel11.7单调案例的直觉

[118] L11.8 A Nonmonoto...

762播放

07:13

L11.8 A Nonmonotonic Examplel11.8一个非单调的例子

[119] L11.9 The PDF of ...

1233播放

07:41

L11.9 The PDF of a Function of Multiple Random Variablesl11.9多个随机变量的函数的PDF

[120] S11.1 SimulationS...

1438播放

12:34

S11.1 SimulationS11.1模拟

[121] L12.1 Lecture Ove...

583播放

01:28

L12.1 Lecture OverviewL12.1讲座概述

[122] L12.2 The Sum of ...

832播放

07:51

L12.2 The Sum of Independent Discrete Random VariablesL12.2独立离散随机变量的总和

[123] L12.3 The Sum of ...

1025播放

06:44

L12.3 The Sum of Independent Continuous Random VariablesL12.3独立连续随机变量的总和

[124] L12.4 The Sum of ...

905播放

03:09

L12.4 The Sum of Independent Normal Random VariablesL12.4独立正常随机变量的总和

[125] L12.5 CovarianceL...

1129播放

05:53

L12.5 CovarianceL12.5协方差

[126] L12.6 Covariance ...

1588播放

05:47

L12.6 Covariance PropertiesL12.6协方差性质

[127] L12.7 The Varianc...

697播放

05:35

L12.7 The Variance of the Sum of Random Variablesl12.7随机变量和随机变量的差异

[128] L12.8 The Correla...

1053播放

07:02

L12.8 The Correlation CoefficientL12.8相关系数

[129] L12.9 Proof of Ke...

636播放

03:51

L12.9 Proof of Key Properties of the Correlation CoefficientL12.9相关系数的关键特性证明

[130] L12.10 Interpreti...

1139播放

05:49

L12.10 Interpreting the Correlation CoefficientL12.10解释相关系数

[131] L12.11 Correlatio...

643播放

06:21

L12.11 Correlations MatterL12.11相关性问题

[132] L13.1 Lecture Ove...

910播放

01:46

L13.1 Lecture OverviewL13.1讲座概述

[133] L13.2 Conditional...

1554播放

04:30

L13.2 Conditional Expectation as a Random VariableL13.2条件期望作为随机变量

[134] L13.3 The Law of ...

659播放

03:57

L13.3 The Law of Iterated ExpectationsL13.3迭代期望的法律

[135] L13.4 Stick-Break...

916播放

03:52

L13.4 Stick-Breaking Revisitedl13.4重新审视粘性

[136] L13.5 Forecast Re...

999播放

04:37

L13.5 Forecast RevisionsL13.5预测修订

[137] L13.6 The Conditi...

1246播放

05:01

L13.6 The Conditional Variancel13.6条件方差

[138] L13.7 Derivation ...

1096播放

04:53

L13.7 Derivation of the Law of Total VarianceL13.7总方差定律的推导

[139] L13.8 A Simple Ex...

1075播放

06:28

L13.8 A Simple Examplel13.8一个简单的例子

[140] L13.9 Section Mea...

620播放

09:03

L13.9 Section Means and VariancesL13.9部分含义和差异

[141] L13.10 Mean of th...

1412播放

06:25

L13.10 Mean of the Sum of a Random Number of Random VariablesL13.10随机数量的随机变量总和的平均值

[142] L13.11 Variance o...

1566播放

05:09

L13.11 Variance of the Sum of a Random Number of Random Variablesl13.11随机数量的随机数量的差异

[143] S13.1 Conditional...

1773播放

08:12

S13.1 Conditional Expectation PropertiesS13.1条件期望属性

[144] L14.1 Lecture Ove...

1013播放

02:09

L14.1 Lecture OverviewL14.1讲座概述

[145] L14.2 Overview of...

752播放

05:16

L14.2 Overview of Some Application DomainsL14.2某些应用领域的概述

[146] L14.3 Types of In...

1419播放

05:23

L14.3 Types of Inference ProblemsL14.3推理问题的类型

[147] L14.4 The Bayesia...

1221播放

09:47

L14.4 The Bayesian Inference FrameworkL14.4贝叶斯推理框架

[148] L14.5 Discrete Pa...

1775播放

06:45

L14.5 Discrete Parameter, Discrete ObservationL14.5离散参数，离散观察

[149] L14.6 Discrete Pa...

1379播放

04:34

L14.6 Discrete Parameter, Continuous ObservationL14.6离散参数，连续观察

[150] L14.7 Continuous ...

1291播放

03:45

L14.7 Continuous Parameter, Continuous ObservationL14.7连续参数，连续观察

[152] L14.9 Inferring t...

652播放

09:29

L14.9 Inferring the Unknown Bias of a Coin - Point EstimatesL14.9推断硬币估计的未知偏差

[153] L14.10 SummaryL14...

1419播放

05:40

L14.10 SummaryL14.10摘要总结

[154] S14.1 The Beta Fo...

1420播放

10:23

S14.1 The Beta FormulaS14.1 Beta公式

[155] L15.1 Lecture Ove...

685播放

01:58

L15.1 Lecture OverviewL15.1讲座概述

[156] L15.2 Recognizing...

632播放

07:14

L15.2 Recognizing Normal PDFsL15.2识别正常的PDF

[157] L15.3 Estimating ...

781播放

08:17

L15.3 Estimating a Normal Random Variable in the Presence of Additive NoiseL15.3在存在附加噪声时估计正常随机变量

[158] L15.4 The Case of...

1192播放

13:46

L15.4 The Case of Multiple Observationsl15.4多重观察的情况

[159] L15.5 The Mean Sq...

1399播放

13:01

L15.5 The Mean Squared ErrorL15.5平均平方误差

[160] L15.6 Multiple Pa...

1344播放

10:32

L15.6 Multiple Parameters; Trajectory Estimationl15.6多个参数;轨迹估计

[161] L15.7 Linear Norm...

946播放

05:11

L15.7 Linear Normal ModelsL15.7线性正常模型

[162] L15.8 Trajectory ...

1251播放

10:54

L15.8 Trajectory Estimation IllustrationL15.8轨迹估计图

[163] L16.1 Lecture Ove...

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01:12

L16.1 Lecture OverviewL16.1讲座概述

[164] L16.2 LMS Estimat...

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06:47

L16.2 LMS Estimation in the Absence of ObservationsL16.2 LMS估计在没有观察的情况下

[165] L16.3 LMS Estimat...

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09:23

L16.3 LMS Estimation of One Random Variable Based on AnotherL16.3基于另一个随机变量的LMS估计

[166] L16.4 LMS Perform...

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04:31

L16.4 LMS Performance EvaluationL16.4 LMS性能评估

[167] L16.5 Example: Th...

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06:30

L16.5 Example: The LMS EstimateL16.5示例：LMS估计

[168] L16.6 Example Con...

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05:29

L16.6 Example Continued: LMS Performance EvaluationL16.6示例继续：LMS性能评估

[169] L16.7 LMS Estimat...

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05:23

L16.7 LMS Estimation with Multiple Observations or UnknownsL16.7 LMS估计具有多种观察或未知数

[170] L16.8 Properties ...

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05:58

L16.8 Properties of the LMS Estimation ErrorL16.8 LMS估计误差的属性

[171] L17.1 Lecture Ove...

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01:40

L17.1 Lecture OverviewL17.1讲座概述

[172] L17.2 LLMS Formul...

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04:57

L17.2 LLMS FormulationL17.2 LLMS制剂

[173] L17.3 Solution to...

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05:05

L17.3 Solution to the LLMS ProblemL17.3 LLMS问题的解决方案

[174] L17.4 Remarks on ...

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08:01

L17.4 Remarks on the LLMS Solution and on the Error VarianceL17.4 LLMS解决方案的备注以及误差方差

[175] L17.5 LLMS Exampl...

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06:42

L17.5 LLMS ExampleL17.5 LLMS示例

[176] L17.6 LLMS for In...

651播放

11:28

L17.6 LLMS for Inferring the Parameter of a CoinL17.6 LLM，用于推断硬币参数

[177] L17.7 LLMS with M...

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06:53

L17.7 LLMS with Multiple ObservationsL17.7 LLM具有多种观察

[178] L17.8 The Simples...

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05:05

L17.8 The Simplest LLMS Example with Multiple ObservationsL17.8具有多个观察的最简单的LLMS示例

[179] L17.9 The Represe...

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07:02

L17.9 The Representation of the Data Matters in LLMSL17.9 LLMS中数据重要事项的表示

[180] L18.1 Lecture Ove...

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01:56

L18.1 Lecture OverviewL18.1讲座概述

[181] L18.2 The Markov ...

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10:21

L18.2 The Markov InequalityL18.2马尔可夫不等式

[182] L18.3 The Chebysh...

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05:56

L18.3 The Chebyshev InequalityL18.3 Chebyshev不平等

[183] L18.4 The Weak La...

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07:30

L18.4 The Weak Law of Large Numbersl18.4大数字的弱法

[184] L18.5 Pollingl18....

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08:11

L18.5 Pollingl18.5轮询

[185] L18.6 Convergence...

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08:27

L18.6 Convergence in ProbabilityL18.6概率的收敛性

[186] L18.7 Convergence...

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08:04

L18.7 Convergence in Probability ExamplesL18.7概率实施例中的收敛

[187] L18.8 Related Top...

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06:43

L18.8 Related TopicsL18.8相关主题

[188] S18.1 Convergence...

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10:12

S18.1 Convergence in Probability of the Sum of Two Random VariablesS18.1在两个随机变量的总和中的概率收敛

[189] S18.2 Jensen's In...

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12:18

S18.2 Jensen's InequalityS18.2 Jensen的不平等

[190] S18.3 Hoeffding's...

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18:27

S18.3 Hoeffding's InequalityS18.3 Hoeffding的不平等

[191] L19.1 Lecture Ove...

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01:49

L19.1 Lecture OverviewL19.1讲座概述

[192] L19.2 The Central...

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06:57

L19.2 The Central Limit TheoremL19.2中央极限定理

[193] L19.3 Discussion ...

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08:59

L19.3 Discussion of the CLTL19.3 CLT的讨论

[194] L19.4 Illustratio...

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02:53

L19.4 Illustration of the CLTL19.4 CLT的插图

[195] L19.5 CLT Example...

1324播放

13:56

L19.5 CLT ExamplesL19.5 CLT示例

[196] L19.6 Normal Appr...

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11:52

L19.6 Normal Approximation to the BinomialL19.6二项式的正常近似

[197] L19.7 Polling Rev...

1413播放

13:53

L19.7 Polling RevisitedL19.7重新审视轮询

[198] L20.1 Lecture Ove...

1429播放

02:45

L20.1 Lecture OverviewL20.1讲座概述

[199] L20.2 Overview of...

1394播放

10:59

L20.2 Overview of the Classical Statistical FrameworkL20.2古典统计框架概述

[200] L20.3 The Sample ...

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04:57

L20.3 The Sample Mean and Some TerminologyL20.3样本意味着和一些术语

[201] L20.4 On the Mean...

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06:53

L20.4 On the Mean Squared Error of an EstimatorL20.4关于估计器的平均平均误差

[202] L20.5 Confidence ...

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05:03

L20.5 Confidence Intervalsl20.5置信区间

[203] L20.6 Confidence ...

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04:26

L20.6 Confidence Intervals for the Estimation of the MeanL20.6估计平均值的置信区间

[204] L20.7 Confidence ...

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06:12

L20.7 Confidence Intervals for the Mean, When the Variance is UnknownL20.7当方差未知时平均值的置信区间

[205] L20.8 Other Natur...

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04:36

L20.8 Other Natural EstimatorsL20.8其他自然估算

[206] L20.9 Maximum Lik...

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06:31

L20.9 Maximum Likelihood EstimationL20.9最大似然估计

[207] L20.10 Maximum Li...

1331播放

10:19

L20.10 Maximum Likelihood Estimation ExamplesL20.10最大似然估计例子

[208] L21.1 Lecture Ove...

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02:01

L21.1 Lecture OverviewL21.1讲座概述

[209] L21.2 The Bernoul...

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04:20

L21.2 The Bernoulli ProcessL21.2 Bernoulli进程

[210] L21.3 Stochastic ...

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06:20

L21.3 Stochastic ProcessesL21.3随机过程

[211] L21.4 Review of K...

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02:19

L21.4 Review of Known Properties of the Bernoulli ProcessL21.4伯努利进程的已知属性审查

[212] L21.5 The Fresh S...

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11:25

L21.5 The Fresh Start PropertyL21.5新的开始属性

[213] L21.6 Example: Th...

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04:15

L21.6 Example: The Distribution of a Busy PeriodL21.6示例：繁忙时期的分布

[214] L21.7 The Time of...

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08:11

L21.7 The Time of the K-th ArrivalL21.7千分之一到来的时间

[215] L21.8 Merging of ...

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07:11

L21.8 Merging of Bernoulli ProcessesL21.8伯努利流程的合并

[216] L21.9 Splitting a...

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05:53

L21.9 Splitting a Bernoulli ProcessL21.9分裂伯努利流程

[217] L21.10 The Poisso...

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06:11

L21.10 The Poisson Approximation to the BinomialL21.10泊松近似于二项式

[218] L22.1 Lecture Ove...

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01:30

L22.1 Lecture OverviewL22.1讲座概述

[219] L22.2 Definition ...

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05:06

L22.2 Definition of the Poisson ProcessL22.2泊松过程的定义

[220] L22.3 Application...

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03:02

L22.3 Applications of the Poisson ProcessL22.3泊松过程的应用

[221] L22.4 The Poisson...

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08:00

L22.4 The Poisson PMF for the Number of ArrivalsL22.4泊松PMF用于抵达的人数

[222] L22.5 The Mean an...

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03:21

L22.5 The Mean and Variance of the Number of Arrivalsl22.5到来的数量的平均值和方差

[223] L22.6 A Simple Ex...

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03:06

L22.6 A Simple Examplel22.6一个简单的例子

[224] L22.7 Time of the...

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10:40

L22.7 Time of the K-th ArrivalL22.7 k-th到来的时间

[225] L22.8 The Fresh S...

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10:33

L22.8 The Fresh Start Property and Its ImplicationsL22.8新的开始属性及其含义

[226] L22.9 Summary of ...

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02:33

L22.9 Summary of ResultsL22.9结果摘要

[227] L22.10 An Example...

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14:07

L22.10 An ExampleL22.10一个例子

[228] L23.1 Lecture Ove...

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01:38

L23.1 Lecture OverviewL23.1讲座概述

[229] L23.2 The Sum of ...

950播放

04:02

L23.2 The Sum of Independent Poisson Random VariablesL23.2独立泊松随机变量的总和

[230] L23.3 Merging Ind...

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08:21

L23.3 Merging Independent Poisson ProcessesL23.3合并独立泊松过程

[231] L23.4 Where is an...

1339播放

04:59

L23.4 Where is an Arrival of the Merged Process Coming From?L23.4合并进程的到达来自哪里？

[232] L23.5 The Time Un...

1113播放

11:24

L23.5 The Time Until the First (or last) Lightbulb Burns Outl23.5第一个（或最后）灯泡燃烧的时间

[233] L23.6 Splitting a...

820播放

05:05

L23.6 Splitting a Poisson ProcessL23.6分裂泊松过程

[234] L23.7 Random Inci...

943播放

09:09

L23.7 Random Incidence in the Poisson ProcessL23.7泊松过程中的随机发病率

[235] L23.8 Random Inci...

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04:35

L23.8 Random Incidence in a Non-Poisson ProcessL23.8非泊松过程中的随机发病率

[236] L23.9 Different S...

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03:58

L23.9 Different Sampling Methods can Give Different ResultsL23.9不同的抽样方法可以给出不同的结果

[237] S23.1 Poisson Ver...

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08:55

S23.1 Poisson Versus Normal Approximations to the BinomialS23.1泊松与二项式的正常近似

[238] S23.2 Poisson Arr...

922播放

09:36

S23.2 Poisson Arrivals During an Exponential IntervalS23.2在指数间隔期间泊松抵达

[239] L24.1 Lecture Ove...

1344播放

01:58

L24.1 Lecture OverviewL24.1讲座概述

[240] L24.2 Introductio...

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02:08

L24.2 Introduction to Markov ProcessesL24.2马尔可夫进程简介

[241] L24.3 Checkout Co...

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12:09

L24.3 Checkout Counter ExampleL24.3结账贴面示例

[242] L24.4 Discrete-Ti...

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07:53

L24.4 Discrete-Time Finite-State Markov ChainsL24.4离散时间有限状态马尔可夫链

[243] L24.5 N-Step Tran...

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10:58

L24.5 N-Step Transition ProbabilitiesL24.5 N步转换概率

[244] L24.6 A Numerical...

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09:25

L24.6 A Numerical Example - Part IL24.6一个数字示例 - 第i部分

[245] L24.7 Generic Con...

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05:31

L24.7 Generic Convergence QuestionsL24.7通用融合问题

[246] L24.8 Recurrent a...

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05:36

L24.8 Recurrent and Transient StatesL24.8复发和瞬态状态

[247] L25.1 Brief Intro...

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01:39

L25.1 Brief IntroductionL25.1简介

[248] L25.2 Lecture Ove...

1004播放

01:04

L25.2 Lecture OverviewL25.2讲座概述

[249] L25.3 Markov Chai...

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06:14

L25.3 Markov Chain ReviewL25.3马尔可夫链审查

[250] L25.4 The Probabi...

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L25.4 The Probability of a PathL25.4路径的概率

[251] L25.5 Recurrent a...

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03:25

L25.5 Recurrent and Transient States: ReviewL25.5复发和瞬态状态：审查

[252] L25.6 Periodic St...

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06:48

L25.6 Periodic StatesL25.6定期状态

[253] L25.7 Steady-Stat...

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09:12

L25.7 Steady-State Probabilities and ConvergenceL25.7稳态概率和收敛性

[254] L25.8 A Numerical...

779播放

03:57

L25.8 A Numerical Example - Part IIL25.8一个数值例子 - 第二部分

[255] L25.9 Visit Frequ...

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05:19

L25.9 Visit Frequency Interpretation of Steady-State ProbabilitiesL25.9访问稳态概率的频率解释

[256] L25.10 Birth-Deat...

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08:55

L25.10 Birth-Death Processes - Part IL25.10出生死亡过程 - 第一部分

[257] L25.11 Birth-Deat...

916播放

08:56

L25.11 Birth-Death Processes - Part IIL25.11出生死亡过程 - 第二部分

[258] L26.1 Brief Intro...

959播放

01:40

L26.1 Brief IntroductionL26.1简介

[259] L26.2 Lecture Ove...

864播放

00:39

L26.2 Lecture OverviewL26.2讲座概述

[260] L26.3 Review of S...

1125播放

09:11

L26.3 Review of Steady-State BehaviorL26.3稳态行为审查

[261] L26.4 A Numerical...

1210播放

10:34

L26.4 A Numerical Example - Part IIIL26.4一个数值例子 - 第III部分

[262] L26.5 Design of a...

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18:29

L26.5 Design of a Phone SystemL26.5手机系统的设计

[263] L26.6 Absorption ...

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09:57

L26.6 Absorption ProbabilitiesL26.6吸收概率

[264] L26.7 Expected Ti...

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11:29

L26.7 Expected Time to AbsorptionL26.7预期吸收时间

[265] L26.8 Mean First ...

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08:43

L26.8 Mean First Passage TimeL26.8平均第一次通过时间

[266] L26.9 Gambler's R...

1113播放

11:23

L26.9 Gambler's Ruinl26.9赌徒的毁灭