## Course Description

This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.

## Lecture Notes

LEC # | TOPICS | LECTURE NOTES |
---|---|---|

1 | Probability, Set Operations | (PDF) |

2 | Properties of Probability Finite Sample Spaces, Some Combinatorics | (PDF) |

3 | Multinomial Coefficients, Union of Events | (PDF) |

4 | Matching Problem, Conditional Probability | (PDF) |

5 | Independence of Events | (PDF) |

6 | Solutions to Problem Set 1 | (PDF) |

7 | Bayes' Formula | (PDF) |

8 | Random Variables and Distributions | (PDF) |

9 | Cumulative Distribution Function | (PDF) |

10 | Marginal Distributions | (PDF) |

11 | Conditional Distributions, Multivariate Distributions | (PDF) |

12 | Functions of Random Variables, Convolution | (PDF) |

13 | Functions of Random Variables: Sum, Product, Ratio, Maximum, Change of Variables | (PDF) |

14 | Linear Transformations of Random Vectors, Review of Problem Set 4 | (PDF) |

15 | Review for Exam 1 | (PDF) |

16 | Expectation, Chebyshev's Inequality | (PDF) |

17 | Properties of Expectation, Variance, Standard Deviation | (PDF) |

18 | Law of Large Numbers, Median | (PDF) |

19 | Covariance and Correlation, Cauchy-Schwartz Inequality | (PDF) |

20 | Poisson Distribution, Approximation of Binomial Distribution, Normal Distribution | (PDF) |

21 | Normal Distribution, Central Limit Theorem | (PDF) |

22 | Central Limit Theorem, Gamma Distribution, Beta Distribution | (PDF) |

23 | Estimation Theory, Bayes' Estimators | (PDF) |

24 | Bayes' Estimators | (PDF) |

25 | Maximum Likelihood Estimators | (PDF) |

26 | Chi-square Distribution, t-distribution, Confidence Intervals for Parameters of Normal Distribution | (PDF) |

27 | Confidence Intervals for Parameters of Normal Distribution | (PDF) |

28 | Review for Exam 2 | (PDF) |

29 | Hypotheses Testing, Bayes' Decision Rules | (PDF) |

30 | Most Powerful Test for Two Simple Hypotheses | (PDF) |

31 | t-test | (PDF) |

32 | Two-sample t-test, Goodness-of-fit Tests, Pearson's Theorem | (PDF) |

33 | Simple Goodness-of-fit Test, Composite Hypotheses | (PDF) |

34 | Contingency Tables, Tests of Independence and Homogeneity | (PDF) |

35 | Kolmogorov-Smirnov Goodness-of-fit Test | (PDF) |

36 | Review of Test 2 | (PDF) |

37 | Review for the Final Exam | (PDF) |

## Exams and Solutions

PRACTICE TESTS SOLUTIONS

## No comments:

## Post a Comment