# Math 1610: Probability

## Course documents

## Homework

- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5 [solutions]
- Homework 6 [solutions]
- Homework 7 [solutions]
- Homework 8 [solutions]
- Homework 9 [solutions]

## Exams

## Julia

The code used in this course will be written in Julia, a language designed for fast and interactive technical computing.

### Notebooks

Buffon’s Needle and Bertrand’s Paradox (html) (Jupyter notebook)

Birthday Problem and Binomial Probabilities (html) (Jupyter notebook)

Stirling’s Formula (html) (Jupyter notebook)

Numerical Convolution (html) (Jupyter notebook)

## Topics Schedule

Date | Sections | Topics | |
---|---|---|---|

1 | 2015-09-10 | 1.2 | Discrete probability distributions |

2 | 2015-09-15 | 2.1 | Simulation of continuous probabilities |

3 | 2015-09-17 | 2.2 | Continuous density functions |

4 | 2015-09-22 | 3.1 | Permutations |

5 | 2015-09-24 | 3.2 | Combinations |

6 | 2015-09-29 | 4.1 | Discrete conditional probability |

7 | 2015-10-01 | 4.2,4.3 | Continuous conditional probability, Paradoxes |

8 | 2015-10-06 | 5.1 | Important distributions |

9 | 2015-10-08 | 5.2 | Important densities |

10 | 2015-10-13 | 6.1 | Expected value |

11 | 2015-10-15 | Exam | |

12 | 2015-10-20 | 6.2 | Variance of discrete random variables |

13 | 2015-10-22 | 6.3,7.1 | Expected value and variance of continuous random variables, Sums of discrete random variables |

14 | 2015-10-27 | 7.2,8.1 | Sums of continuous random variables, Law of large numbers (discrete) |

15 | 2015-10-29 | 8.2 | Law of large numbers (continuous) |

16 | 2015-11-03 | 9.1 | Bernoulli trials and the Central Limit Theorem |

17 | 2015-11-05 | 9.2 | CLT -- Discrete Independent Trials |

18 | 2015-11-10 | 9.3 | CLT -- Continuous Independent Trials |

19 | 2015-11-12 | 10.1 | Discrete distributions |

20 | 2015-11-17 | 10.2 | Branching processes |

21 | 2015-11-19 | 10.3 | Continuous densities |

22 | 2015-11-24 | 11.2,11.3 | Absorbing Markov chains, Ergodic Markov chains |

23 | 2015-12-01 | 11.4 | Fundamental limit theorem for Markov chains |

24 | 2015-12-03 | 12.1 | Random walks in Euclidean space |