# Inequalities and Asymptotics

Week 04, Spring 2022

**Start:**Monday, February 7**End:**Friday, February 11

## Summary

This will be our last week reviewing probability concepts. First we’ll look at some useful inequalities. Then we will discuss asymptotics, leading to the central limit theorem.

## Learning Objectives

After completing this week, you are expected to be able to:

*Provide*bounds on probabilities using well known inequalities.*Understand*the difference between convergence in probability and distribution.*Understand*the central limit theorem.*Approximate*probabilities based on asymptotic normality.*Understand*the weak law of large numbers.*Use*the delta method.

## Reading

Source | Section |
---|---|

Wasserman |
4.1 - 4.4 |

Wasserman |
5.1 - 5.7 |

Evans and Rosenthal | 3.6 |

Evans and Rosenthal | 4.1 - 4.6 |

Marden | 8.1 - 8.7 |

Marden | 9.1 - 9.5 |

## Video

Title and Slides | Link | Mirror |
---|---|---|

4.0 - Welcome to Week 04 | 4.0 - YouTube | 4.0 - ClassTranscribe |

4.1 - Inequalities | 4.1 - YouTube | 4.1 - ClassTranscribe |

4.2 - Convergence | 4.2 - YouTube | 4.2 - ClassTranscribe |

4.3 - Central Limit Theorem Proof | 4.3 - YouTube | 4.3 - ClassTranscribe |

## Assignments

**Homework 03**- Source:
`R`

Markdown - Due: Monday, February 14
- Submission: Gradescope
- Solution: Canvas

- Source:

## Office Hours

Staff and Link | Day | Time |
---|---|---|

Zoom with David |
Monday | 5:30 PM - 6:30 PM |

Zoom with Eugene |
Monday | 9:00 PM - 10:00 PM |

Zoom with Eugene |
Thursday | 12:00 PM - 1:00 PM |

Zoom with David |
Thursday | 5:00 PM - 7:00 PM |

Discussion Forum | Any! | Any! |