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Statistics for Applications >> Content Detail



Syllabus



Syllabus

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Prerequisites


Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041)



Topics




Maximum Likelihood Estimators


  • Properties
  • Fisher Information
  • Asymptotic Variance of MLE


Parameters of Normal Distribution


  • Chi-squared and t-Distribution
  • Distribution of the Estimates of Parameters of Normal Distribution
  • Confidence Intervals


Testing Hypotheses


  • t-Tests and F-Tests
  • Bayes Tests
  • Most Powerful Tests (Including Randomized)


Goodness-of-fit Tests


  • Simple Discrete
  • Continuous
  • Composite Goodness-of-fit Tests
  • Independence and Homogeneity Tests
  • Kolmogorov-Smirnov Test


Linear Regression


  • Estimating Parameters
  • Joint Distribution of Estimates
  • Testing Hypotheses about Parameters
  • Confidence and Prediction Intervals
  • Joint Confidence Sets


Multiple Regression, Analyses of Variance and Covariance


  • Distribution of Estimates
  • Testing General Linear Hypotheses


Grading



ACTIVITIESweightS
Ten Problem Sets10 points each
Two Midterm Exams150 points each



Text


Amazon logo DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2002. ISBN: 0201524880.



Calendar


The calendar below provides information on the course's lecture (L) and exam (E) sessions.


SES #TOPICSKEY DATES
L1Overview of some Probability Distributions
L2Maximum Likelihood Estimators
L3Properties of Maximum Likelihood EstimatorsProblem set 1 due
L4Multivariate Normal Distribution and CLT
L5Confidence Intervals for Parameters of Normal DistributionProblem set 2 due
L6Gamma, Chi-squared, Student T and Fisher F DistributionsProblem set 3 due
L7-L8Testing Hypotheses about Parameters of Normal Distribution, t-Tests and F-TestsProblem set 4 due in Ses #L8
L9

Testing Simple Hypotheses

Bayes Decision Rules

Problem set 5 due
E1Exam 1
L10Most Powerful Test for Two Simple Hypotheses
L11Chi-squared Goodness-of-fit Test
L12Chi-squared Goodness-of-fit Test for Composite Hypotheses
L13Tests of Independence and HomogeneityProblem set 6 due
L14Kolmogorov-Smirnov Test
L15-L16Simple Linear RegressionProblem set 7 due
L17-L18Multiple Linear RegressionProblem set 8 due
L19-L20

General Linear Constraints in Multiple Linear Regression

Analysis of Variance and Covariance

Problem set 9 due

Problem set 10 due in Ses #L20

E2Exam 2
L21Classification Problem, AdaBoost Algorithm
L22Review

 








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