### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

### 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

ACTIVITIES | weightS |
---|---|

Ten Problem Sets | 10 points each |

Two Midterm Exams | 150 points each |

### Text

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

### Calendar

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

SES # | TOPICS | KEY DATES |
---|---|---|

L1 | Overview of some Probability Distributions | |

L2 | Maximum Likelihood Estimators | |

L3 | Properties of Maximum Likelihood Estimators | Problem set 1 due |

L4 | Multivariate Normal Distribution and CLT | |

L5 | Confidence Intervals for Parameters of Normal Distribution | Problem set 2 due |

L6 | Gamma, Chi-squared, Student T and Fisher F Distributions | Problem set 3 due |

L7-L8 | Testing Hypotheses about Parameters of Normal Distribution, t-Tests and F-Tests | Problem set 4 due in Ses #L8 |

L9 |
Testing Simple Hypotheses Bayes Decision Rules |
Problem set 5 due |

E1 | Exam 1 | |

L10 | Most Powerful Test for Two Simple Hypotheses | |

L11 | Chi-squared Goodness-of-fit Test | |

L12 | Chi-squared Goodness-of-fit Test for Composite Hypotheses | |

L13 | Tests of Independence and Homogeneity | Problem set 6 due |

L14 | Kolmogorov-Smirnov Test | |

L15-L16 | Simple Linear Regression | Problem set 7 due |

L17-L18 | Multiple Linear Regression | Problem 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 |

E2 | Exam 2 | |

L21 | Classification Problem, AdaBoost Algorithm | |

L22 | Review |