STAT711 | Statistical Theory 1

Fall 2023

Time: Tu/F 11-12:30am at SCB4402

Instructor


Gradings


References


Lecture Notes

No.TopicNotesHomework
1 Basic set theory and probability
2 Counting
3 Conditional probability
4 Independence and random variables
5 Multiple random variables
6 Variance and Standard Deviation Homework 1
7 Probability distributions
8 Probability density functions
9 Examples of probability distributions
10 Poisson and Normal distributions
11 Cumulative distribution functions
12 Marginal and conditional distributions, Independence Homework 2
13 Transformation of random variables
14 Moments and MGF
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