STAT711 | Statistical Theory 1

Fall 2020

Time: Tu/F 11-12:30am in Microsoft Teams

Instructor


Gradings


References


Lecture Notes

LectureTopicNotesHomework
1 Basic set theory and probability Lecture 1
2 Counting Lecture 2
3 Conditional probability Lecture 3
4 Independence and random variables Lecture 4
5 Multiple random variables Lecture 5
6 Variance and Standard Deviation Lecture 6Homework 1
7 Probability distributions Lecture 7
8 Probability density functions Lecture 8
9 Examples of probability distributions Lecture 9
10 Poisson and Normal distributions Lecture 10
11 Cumulative distribution functions Lecture 11
12 Marginal and conditional distributions, Independence Lecture 12Homework 2
13 Transformation of random variables Lecture 13
14 Moments and MGF Lecture 14
15 Random samples Lecture 15
16 Sample mean and sample variance Lecture 16
17 Sufficient statistics Lecture 17
18 Minimal sufficient statistics Lecture 18Homework 3
19 Complete statistics, Basu's theorem Lecture 19
20 Rao-Blackwell theorem, UMVU Lecture 20
21 Maximum Likelihood estimators Lecture 21
22 Cramér-Rao inequality Lecture 22
23 Bayesian inference Lecture 23Homework 4
24 Minimax estimators Lecture 24
25 Neyman-Pearson lemma Lecture 25
26 Monotone likelihood ratio tests Lecture 26
27 Likelihood ratio tests Lecture 27
28 Confidence intervals Lecture 28Homework 5