Difference between revisions of "MAT5373"

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(Created page with "=Mathematical Statistics - MAT4173/5373= {| class="wikitable" | Session || Section || Date || Topic |- | 1 || 1.1 || 6/5/2017 || Populations and Samples |- | 2 || 1.2 || 6/...")
 
 
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=Mathematical Statistics - MAT4173/5373=
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=Mathematical Foundations of Statistics I - MAT4173/5373=
  
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'''Catalog entry'''
  
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''Prerequisite'': [[MAT1213]]/[[MAT1214]] Calculus I.
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''Content'': Mathematical Foundations of Statistics I is an introductory course that covers key concepts in statistics from a mathematical perspective, including populations and samples, descriptive statistics, probability, discrete and continuous distributions, transformations, jointly distributed random variables, covariance and correlation, order statistics, and the Central Limit Theorem. The course equips students with foundational knowledge and techniques for data analysis and statistical modeling in various fields.
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== List of Topics==
  
 
{| class="wikitable"
 
{| class="wikitable"
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| Session || Section || Date || Topic
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| Session || Section || Topic || Pre-requisites
 
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| 1 || 1.1 || 6/5/2017 || Populations and Samples
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| 1 || 1.1 || Populations and Samples ||
 
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| 2 || 1.2 || 6/6/2017 || Pictorial and Tabular Methods in Descriptive Statistics
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| 2 || 1.2 || Pictorial and Tabular Methods in Descriptive Statistics ||
 
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|-
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| 3 || 1.3 || 6/7/2017 || Measures of Location
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| 3 || 1.3 || Measures of Location ||
 
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| 4 || 1.4 || 6/8/2017 || Measures of Variability
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| 4 || 1.4 || Measures of Variability ||
 
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| 5 || 2.1 || 6/9/2017 || Sample Spaces and Events
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| 5 || 2.1 || Sample Spaces and Events ||
 
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| 6 || 2.2 || 6/12/2017 || Axioms, Interpretations, and Properties of Probability
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| 6 || 2.2 || Axioms, Interpretations, and Properties of Probability ||
 
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| 7 || 2.3 || 6/13/2017 || Counting Techniques
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| 7 || 2.3 || Counting Techniques ||  
 
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| 8 || 2.4 || 6/14/2017 || Conditional Probability
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| 8 || 2.4 || Conditional Probability ||  
 
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| 9 || 2.5 || 6/15/2017 || Independence
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| 9 || 2.5 || Independence ||  
 
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| 10 || -- || 6/16/2017 || REVIEW
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| 10 || colspan="3" | REVIEW  
 
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| 11 || -- || 6/19/2017 || TEST 1
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| 11 || colspan="3" |   TEST 1
 
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| 12 || 3.1 || 6/20/2017 || Random Variables
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| 12 || 3.1 || Random Variables ||  
 
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| 13 || 3.2 || 6/21/2017 || Probability Distributions for Discrete Random Variables
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| 13 || 3.2 || Probability Distributions for Discrete Random Variables ||
 
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| 14 || 3.3 || 6/22/2017 || Expected Values of Discrete Random Variables
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| 14 || 3.3 || Expected Values of Discrete Random Variables ||
 
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| 15 || 3.4 || 6/23/2017 || Moments and Moment Generating Functions
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| 15 || 3.4 || Moments and Moment Generating Functions ||
 
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| 16 || 3.5 || 6/26/2017 || The Binomial Probability Distribution
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| 16 || 3.5 || The Binomial Probability Distribution ||
 
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| 17 || 3.6 || 6/27/2017 || Hypergeometric and Negative Binomial Distributions
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| 17 || 3.6 || Hypergeometric and Negative Binomial Distributions ||
 
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| 18 || 3.7 || 6/28/2017 || The Poisson Probability Distribution
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| 18 || 3.7 || The Poisson Probability Distribution ||
 
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| 19 || 4.1 || 6/29/2017 || Probability Density Functions and Cumulative Distribution Functions
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| 19 || 4.1 || Probability Density Functions and Cumulative Distribution Functions ||
 
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| 20 || 4.2 || 6/30/2017 || Expected Values and Moment Generating Functions
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| 20 || 4.2 || Expected Values and Moment Generating Functions ||
 
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| 21 || 4.3 || 7/3/2017 || The Normal Distribution
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| 21 || 4.3 || The Normal Distribution ||
 
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| 22 || 4.4 || 7/5/2017 || The Gamma Distribution and Its Relatives
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| 22 || 4.4 || The Gamma Distribution and Its Relatives ||
 
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| 23 || 4.5 || 7/6/2017 || Other Continuous Distributions
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| 23 || 4.5 || Other Continuous Distributions ||
 
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| 24 || 4.6 || 7/7/2017 || Probability Plots
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| 24 || 4.6 || Probability Plots ||  
 
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| 25 || 4.7 || 7/10/2017 || Transformations of a Random Variable
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| 25 || 4.7 || Transformations of a Random Variable ||
 
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| 26 || -- || 7/11/2017 || REVIEW
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| 26 || colspan="3" | REVIEW
 
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| 27 || -- || 7/12/2017 || TEST 2
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| 27 || colspan="3" | TEST 2
 
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| 28 || 5.1 || 7/13/2017 || Jointly Distributed Random Variables
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| 28 || 5.1 || Jointly Distributed Random Variables ||
 
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| 29 || 5.2 || 7/14/2017 || Expected Values, Covariance, and Correlation
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| 29 || 5.2 || Expected Values, Covariance, and Correlation ||
 
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| 30 || 5.3 || 7/17/2017 || Conditional Distributions
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| 30 || 5.3 || Conditional Distributions ||  
 
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| 31 || 5.4 || 7/18/2017 || Transformations of Random Variables
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| 31 || 5.4 || Transformations of Random Variables ||
 
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| 32 || 5.5 || 7/19/2017 || Order Statistics
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| 32 || 5.5 || Order Statistics ||  
 
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| 33 || 6.1 || 7/20/2017 || Statistics and Their Distributions
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| 33 || 6.1 || Statistics and Their Distributions ||
 
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| 34 || 6.2 || 7/21/2017 || The Distribution of the Sample Mean
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| 34 || 6.2 || The Distribution of the Sample Mean ||
 
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| 35 || 6.3 || 7/24/2017 || The Mean, Variance, and MGF for Several Variables
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| 35 || 6.3 || The Mean, Variance, and MGF for Several Variables ||
 
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| 36 || 6.4 || 7/25/2017 || Distributions Based on a Normal Random Sample
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| 36 || 6.4 || Distributions Based on a Normal Random Sample ||
 
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| 37 || 6.5 || 7/26/2017 || Proof of the Central Limit Theorem
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| 37 || 6.5 || Proof of the Central Limit Theorem ||
 
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| 38 || -- || 7/27/2017 || REVIEW
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| 38 || colspan="3" | REVIEW  
 
|}
 
|}

Latest revision as of 21:44, 25 April 2023

Mathematical Foundations of Statistics I - MAT4173/5373

Catalog entry

Prerequisite: MAT1213/MAT1214 Calculus I.

Content: Mathematical Foundations of Statistics I is an introductory course that covers key concepts in statistics from a mathematical perspective, including populations and samples, descriptive statistics, probability, discrete and continuous distributions, transformations, jointly distributed random variables, covariance and correlation, order statistics, and the Central Limit Theorem. The course equips students with foundational knowledge and techniques for data analysis and statistical modeling in various fields.

List of Topics

Session Section Topic Pre-requisites
1 1.1 Populations and Samples
2 1.2 Pictorial and Tabular Methods in Descriptive Statistics
3 1.3 Measures of Location
4 1.4 Measures of Variability
5 2.1 Sample Spaces and Events
6 2.2 Axioms, Interpretations, and Properties of Probability
7 2.3 Counting Techniques
8 2.4 Conditional Probability
9 2.5 Independence
10 REVIEW
11 TEST 1
12 3.1 Random Variables
13 3.2 Probability Distributions for Discrete Random Variables
14 3.3 Expected Values of Discrete Random Variables
15 3.4 Moments and Moment Generating Functions
16 3.5 The Binomial Probability Distribution
17 3.6 Hypergeometric and Negative Binomial Distributions
18 3.7 The Poisson Probability Distribution
19 4.1 Probability Density Functions and Cumulative Distribution Functions
20 4.2 Expected Values and Moment Generating Functions
21 4.3 The Normal Distribution
22 4.4 The Gamma Distribution and Its Relatives
23 4.5 Other Continuous Distributions
24 4.6 Probability Plots
25 4.7 Transformations of a Random Variable
26 REVIEW
27 TEST 2
28 5.1 Jointly Distributed Random Variables
29 5.2 Expected Values, Covariance, and Correlation
30 5.3 Conditional Distributions
31 5.4 Transformations of Random Variables
32 5.5 Order Statistics
33 6.1 Statistics and Their Distributions
34 6.2 The Distribution of the Sample Mean
35 6.3 The Mean, Variance, and MGF for Several Variables
36 6.4 Distributions Based on a Normal Random Sample
37 6.5 Proof of the Central Limit Theorem
38 REVIEW
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