# Graduate Level: Intro to Probability and Statistics

Jump to navigation
Jump to search

# Lecture Notes

01 | Probability Theory, Probability Space, Random Variables, Cumulative Distribution Function(section-by-section | single page) |

10 | Finding UMVU Estimators, Complete Statistics, Cramér-Rao Lower Bound(section-by-section | single page) |

02 | Random Variables, Leibniz Rule and Transformations of RVs(section-by-section | single page) |

11 | Hypothesis Testing, Power Function, Selecting the Critical Value(section-by-section | single page) |

03 | Expectations of RVs and Moments(section-by-section | single page) |

12 | Hypothesis Testing (cont.), LRT, LM, Wald, Test Equivalence, Test Optimality(section-by-section | single page) |

04 | Examples of Distributions(section-by-section | single page) |

13 | Test Optimality (cont.), 2-sided tests, p-values, Interval Estimation(section-by-section | single page) |

05 | Families of Distributions, Chebychev's Inequality, Multiple Random Variables(section-by-section | single page) |

14 | Convergence, Law of Large Numbers, Central Limit Theorem, Delta Method(section-by-section | single page) |

06 | Multiple RVs (cont.), Conditional Moments, LIE, CVI, Covariance and Correlation, Some Inequalities(section-by-section | single page) |

15 | Asymptotic Properties of ML Estimators(section-by-section | single page) |

07 | Random Sample, Statistics, Statistical Inference(section-by-section | single page) |

16 | Bayesian Estimation(section-by-section | single page) |

08 | Point Estimation, Method of Moments, Maximum Likelihood(section-by-section | single page) |

17 | OLS, Normal Linear Model, Asymptotic Properties(section-by-section | single page) |

09 | Point Estimation (cont.), Evaluating Estimators, UMVU, Sufficient Statistics, Rao-Blackwell(section-by-section | single page) |

18 | Multicollinearity, Partitioned Regression, Gauss-Markov Theorem(section-by-section | single page) |