Introduction to Probability and Mathematical Statistics

Mathematics

Tác giả: Elliot Gangaram
Nhà xuất bản: Queens College
Nguồn: LibreTexts
Giấy phép: CC BY
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 60 mục

01: Week 1
1.01: Basic Set Theory
1.02: The Three Axioms of Probability
1.03: Basic Propositions in Probability
02: Week 2
2.01: Applications
2.02: Introduction to Counting
2.03: Permutations
2.3.01: The Multinomial Part 1
03: Week 3
3.01: Combinations
3.02: The Multinomial
3.2.01: The Multinomial Part 2
04: Week 4
4.01: Simple Sample Spaces
4.02: Overcounting
05: Week 5
5.01: Review 1
5.02: Exam 1
06: Week 6
6.01: Conditional Probabilities
6.02: Independence
07: Week 7
7.01: Bayes' Theorem
08: Week 8
8.01: Discrete Random Variables
8.02: The Cumulative Distribution Function
8.03: Expected Values
09: Week 9
9.01: Variances
9.02: The Uniform Random Variable
9.03: The Bernoulli and Binomial Random Variables
9.04: The Geometric and Negative Binomial Random Variables
9.05: The Poisson Random Variable
10: Week 10
10.01: Review 2
10.02: Exam 2
11: Week 11
11.01: Continuous Random Variables
11.02: The Uniform Continuous Distribution
11.03: The Exponential Distribution
11.04: The Normal Distribution
12: Week 12
12.01: The Central Limit Theorem
13: Week 13
13.01: Inferential Statistics
13.02: Confidence Intervals
14: Week 14
14.01: Procedures of Hypotheses Testing and the Scientific Method
14.02: Formulate General Research Questions
14.03: Design Research Hypotheses and Experiment
14.04: Collect and Analyze Experimental Data
14.05: Report Conclusions in Nonstatistical Language
14.06: Test of Mean vs. Hypothesized Value A Complete Example
14.07: Type II Error and Statistical Power
14.08: New Models for One Population Inference Similar Procedures
14.09: The pvalue- Misconceptions and Proper Usage
15: Week 15
15.01: Review 3
15.02: Final Exam