Course Overview
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Course Synopsis
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Inferential Statistics is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
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Course Learning Outcomes
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At the end of course student should be able to understand:
- Use mathematical and statistical techniques to solve well-defined problems and present their mathematical work, both in oral and written format.
- Propose new statistical models and suggest possible software packages and/or computer programming to find solutions to these models.
- Continue to acquire statistical knowledge and skills appropriate to professional activities.
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Course Calendar
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Week 01
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1
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Statistical Inference and its importance
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2
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Introduction to random sampling
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3
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Statistic with examples
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4
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Methods of drawing samples
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5
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Sums of the random variables from a random sample
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6
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Some results about Random Variable
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7
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Some results about random variables
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8
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Moment generating function
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9
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Exact sampling distribution: Chi-square distribution
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10
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Some more results(Exact sampling distribution: Chi-square distribution)
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11
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Exact sampling distribution: Normal distribution
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12
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Some more results1(Exact sampling distribution: Normal distribution)
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13
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Some more results2(Exact sampling distribution: Normal distribution)
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14
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Exact sampling distribution: t-dsitribution
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15
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Exact sampling distribution: F-dsitribution
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16
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Reciprocal property of F-distribution
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17
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Application of Chi-Square t &F distribution
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Week 02
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19
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Distribution of order statistics
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20
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Distribution of order statistics: Example
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21
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joint distribution of i-th and j-th order statistics
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22
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Application(joint distribution )
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23
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Chebychev's Inequality and its usage
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25
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Convergence in probability
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26
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Week law of large number
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27
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Almost sure convergence
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28
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Strong law of large number
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29
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Convergence in distribution
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31
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Generating a random sample
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32
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Direct method with example
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33
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Indirect method with example
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34
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Direct Method:application
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35
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Indirect Method:application
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Week 03
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39
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Methods of point estimation
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42
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Maximum Likelihood (ML) method
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49
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Regularity conditions:Assumptions
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51
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Remarks(Fisher Information)
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52
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Example(Fisher Information)
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53
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Information for a location family
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54
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Example(Information for a location family)
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55
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Application(Fisher Information)
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56
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Application(ChiSqaure)
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Week 04
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60
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Newton Raphson's method
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Quiz 1
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61
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Example(Newton Raphson's method)
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67
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Properties of moment estimator
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73
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Application(Posterior dist)
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74
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Application(Jeffreys prior )
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75
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Application(Bayes estimate )
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Assignment 1
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76
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Bayesian predictive distribution
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Week 05
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77
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Properties of point estimate
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82
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Application(Unbiasedness)
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86
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Application from exercise
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Week 06
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90
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Application: EfficiencyQ 6.2.7(b)
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91
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Application: Efficiency Q 6.2.7(c)
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92
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Application:Efficiency Q 6.2.8(a)
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93
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Application: Efficiency Q 6.2.8(b)
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94
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Application:Efficiency Q 6.2.8(c)
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95
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Asymptotically efficiency
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96
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Application: Efficiency Q 6.2.11
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100
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Best unbiased estimator
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Week 07
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102
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Carmer-Rao Inequality
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103
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Corollary:Carmer-Rao Inequality
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Quiz 2
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104
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Example(Carmer-Rao Inequality)
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105
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Corollary(Carmer-Rao Inequality )
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106
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example1(Carmer-Rao Inequality)
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107
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example 2(Carmer-Rao Inequality)
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108
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Application(Rao-Cramer lower bound )
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109
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Application(Rao-Cramer lower bound)
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110
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MLE are asymptotically efficent
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Week 08
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116
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Application1(Sufficency)
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117
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Application2(Sufficency)
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118
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Application3(Sufficency)
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119
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Neyman-Fisher factorization theorem
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120
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Example1:Neyman-Fisher factorization theorem
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121
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Example2:Neyman-Fisher factorization theorem
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Mid Term
Week 09
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122
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Properties of sufficient statistics
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124
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Application(Sufficency)
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126
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Sufficiency and Unbiasedness
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127
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Rao-Blackwell theorem
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129
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Uniqueness of Unbised estimator
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130
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Continue(uniqueness of unbised estimator)
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131
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UMVUE in Multiparameter Case
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Week 10
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134
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Example 1:Completeness
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135
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Example 2:Completeness
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136
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Application1 :Completeness
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137
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Application2:Completeness
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138
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Lehmann-Scheffe theorem
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141
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Application:Completeness
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Week 11
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144
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Example:Exponential family
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148
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Example:Jointly sufficient
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149
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Application:Jointly sufficient
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GDB
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151
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Example:Minimal sufficiency
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153
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Example:Ancillary Statistics
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156
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Location-Scale problems
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Week 12
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157
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Bayesian point estimate
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158
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Example:Bayes Estimate
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159
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Application:Bayes Estimate
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160
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Unbiasdness Bayes estimates
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161
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Testing of Hypothesis
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165
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Example:Best critical region
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ASSIGNMENT 2
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167
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Application1:Neyman-Pearson lemma
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168
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Application2:Neyman-Pearson lemma
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Week 13
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169
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Uniformly most powerful tests
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170
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Example1:Uniformly most powerful tests
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171
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Example2:Uniformly most powerful tests
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173
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Likelihood ratio tests
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174
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Example:1Likelihood ratio tests
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175
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Example:2Likelihood ratio tests
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176
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Likelihood Ratio Test for the exponential distribution
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177
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Example1:Likelihood Ratio Test for the exponential distribution
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Quiz 3
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178
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Example2:Likelihood Ratio Test for the exponential distribution
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Week 14
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180
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Example:Wilks Theorem
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181
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Application1:Wilks Theorem
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182
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Application2:Wilks Theorem
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183
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LR for Binomial Proportion
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184
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Example1:LR for Binomial Proportion
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185
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Example2:LR for Binomial Proportion
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186
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Sequentional probability ratio test
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187
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Example1:Sequentional probability ratio test
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188
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Example2:Sequentional probability ratio test
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189
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Application:Sequentional probability ratio test
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Week 15
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190
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Bootstrap testing procedures
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191
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Example:Bootstrap testing procedures
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194
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Procedure of Finding Interval Estimation
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195
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Confidence interval for mean when population variance is known
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196
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Confidence interval for mean when population variance is unknown
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197
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Confidence interval for population variance when polulation mean is unknown
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198
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Confidence interval for pouplation proportion
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199
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Application:Confidence interval for pouplation proportion
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Final Term
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