STAT 350: Introduction to Statistics

Orientation

  • Course Introduction & Overview
    • Why Statistics? Why Now?
    • Course Roadmap
    • A Clear Note on Using AI
    • Getting Started: A Checklist
      • Homework Assignments on Edfinity
      • Miscellaneous Tips

Exam Information

  • Course Examinations
    • General Exam Policies
      • Exam 1
        • Exam Locations by Section
        • Exam Coverage
        • Preparation Materials
      • Exam 2
        • Exam Locations by Section
        • Exam Coverage
        • Additional Resources
        • Preparation Materials
      • Final Exam
        • About the Final Exam
        • Required Review Materials
        • Post Exam 2 Preparation Materials
        • Study Guide Resource

Worksheets

  • Course Worksheets
    • Pedagogical Philosophy
    • Implementation Guidelines
    • Why These Worksheets Matter
    • The Critical Role of Simulation
    • Worksheets
      • Worksheet 1: Exploring Data with R
        • Introduction
        • Part 1: Loading and Understanding the Dataset
        • Part 2: Initial Data Exploration
        • Part 3: Frequency Tables
        • Part 4: Univariate Analysis of Uptake
        • Part 5: Grouped Statistics with tapply
        • Part 6: Comparative Visualization by Type
        • Part 7: Exploring the Concentration Effect
        • Part 8: Advanced Visualization with Multiple Categories
        • Reference: Key Functions
        • Submission Guidelines
      • Worksheet 2: Set Theory and Probability Fundamentals
        • Introduction
        • Part 1: Set Theory Foundations
        • Part 2: Probability Axioms
        • Part 3: Applying Probability Rules
        • Part 4: The Inclusion-Exclusion Principle
        • Simulation Exercise
        • Key Takeaways
        • Submission Guidelines
      • Worksheet 3: Conditional Probability and Bayes’ Theorem
        • Introduction
        • Part 1: Understanding Conditional Probability
        • Part 2: Tree Diagrams and Sequential Sampling
        • Part 3: Bayes’ Theorem and Sequential Updating
        • Key Takeaways
      • Worksheet 4: Independence and Random Variables
        • Part 1: Independence Property
        • Part 2: Independent vs. Mutually Exclusive Events
        • Part 3: Introduction to Random Variables
        • Part 4: Probability Mass Functions
        • Part 5: Joint Probability Mass Functions
        • Key Takeaways
      • Worksheet 5: Expected Value and Variance
        • Introduction
        • Part 1: Expected Value and LOTUS
        • Part 2: Variance and Its Properties
        • Part 3: Sums of Random Variables
        • Part 4: Joint Probability Mass Functions
        • Key Takeaways
      • Worksheet 6: Named Discrete Distributions
        • Introduction
        • Part 1: The Bernoulli Distribution
        • Part 2: The Binomial Distribution
        • Part 3: The Poisson Distribution
        • Part 4: Other Named Discrete Distributions
        • Key Takeaways
      • Worksheet 7: Continuous Random Variables
        • Introduction
        • Part 1: Probability Density Functions
        • Part 2: Finding Constants for Valid PDFs
        • Part 3: Expected Value and Variance
        • Part 4: Cumulative Distribution Functions
        • Key Takeaways
      • Worksheet 8: Uniform and Exponential Distributions
        • Introduction
        • Part 1: The Uniform Distribution
        • Part 2: The Exponential Distribution
        • Key Takeaways
      • Worksheet 9: The Normal Distribution
        • Introduction
        • Part 1: The Normal Distribution
        • Part 2: The Empirical Rule
        • Part 3: The Standard Normal Table
        • Part 4: Z-Score Transformation
        • Key Takeaways
      • Worksheet 10: Checking Normality and Introduction to Sampling Distributions
        • Part 1: Checking Normality
        • Part 2: Introduction to Sampling Distributions
        • Key Takeaways

Chapters

  • 1. Introduction to Statistics
    • 1.1. What Is Statistics?
    • 1.2. Probability & Statistical Inference: How Are They Associated?
  • 2. Graphical Summaries
    • 2.1. Data Set Structure and Variable Types
    • 2.2. Tools for Categorical (Qualitative) Data
    • 2.3. Tools for Numerical (Quantitative) Data
    • 2.4. Exploring Quantitative Distributions: Modality, Shape & Outliers
  • 3. Numerical Summaries
    • 3.1. Introduction to Numerical Summaries: Notation and Terminology
    • 3.2. Measures of Central Tendency
    • 3.3. Measures of Variability - Range, Variance, and Standard Deviation
    • 3.4. Measures of Variability - Interquartile Range and Five-Number Summary
    • 3.5. Choosing the Right Measure & Comparing Measures Across Data Sets
  • 4. Probability
    • 4.1. Basic Set Theory
    • 4.2. Probability
    • 4.3. Conditional Probability
    • 4.4. Law of Total Probability and Bayes’ Rule
    • 4.5. Bayesian Updating: Sequential Learning
    • 4.6. Independence of Events
  • 5. Discrete Distributions
    • 5.1. Discrete Random Variables and Probability Mass Distributions
    • 5.2. Joint Probability Mass Functions
    • 5.3. Expected Value of a Discrete Random Variable
    • 5.4. Varianace of a Discrete Random Variable
    • 5.5. Covariance of Dependent Random Variables
    • 5.6. The Binomial Distribution
    • 5.7. Poisson Distribution
  • 6. Continuous Distributions
    • 6.1. Continuous Random Variables and Probability Density Functions
    • 6.2. Expected Value and Variance of Continuous Random Variables
    • 6.3. Cumulative Distribution Functions
    • 6.4. Normal Distribution
    • 6.5. Uniform Distribution
    • 6.6. Exponential Distribution
  • 7. Sampling Distributions
    • 7.1. Statistics and Sampling Distributions
    • 7.2. Sampling Distribution for the Sample Mean
    • 7.3. The Central Limit Theorem (CLT)
    • 7.4. Discrete Random Variables and the CLT
  • 8. Experimental Design
    • 8.1. Experimental and Sampling Designs
    • 8.2. Experimental Design Principles
    • 8.3. Basic Types of Experimental Design
    • 8.4. Addressing Potential Flaws in Experimental Design
    • 8.5. Examples of Experimental Design
    • 8.6. Sampling Design
    • 8.7. Sampling Bias
  • 9. Confidence Intervals and Bounds
    • 9.1. Introduction to Statistical Inference
    • 9.2. Confidence Intervals for the Population Mean, When σ is Known
    • 9.3. Precision of a Confidence Interval and Sample Size Calculation
    • 9.4. Confidence Bounds for the Poulation Mean When σ is Known
    • 9.5. Confidence Intervals and Bounds When σ is Unknown
  • 10. Hypothesis Testing
    • 10.1. Type I Error, Type II Error, and Power
    • 10.2. Hypothesis Test for the Population Mean When σ is Known
    • 10.3. Hypothesis Test for the Population Mean When σ Is Unknown
    • 10.4. P-values, Statistical Significance, and Formal Conclusion
  • 11. Two Sample Procedures
    • 11.1. Confidence Interval/Bound and Hypothesis Test for Two Samples
    • 11.2. Comparing the Means of Two Independent Populations - Population Variances Are Known
    • 11.3. Comparing the Means of Two Independent Populations - Pooled Variance Estimator
    • 11.4. Comparing the Means of Two Independent Populations - No Equal Variance Assumption
    • 11.5. Analyzing the Mean of Paired Differences Between two Dependent Populations
  • 12. ANOVA
    • 12.1. Introduction to One-Way ANOVA
    • 12.2. Different Sources of Variability in an ANOVA Model
    • 12.3. One-Way ANOVA F-Test and Its Relationship to Two-Sample t-Tests
    • 12.4. Multiple Comparison Procedures and Family-Wise Error Rates
  • 13. Simple Linear Regression
    • 13.1. Introduction to Linear Regression: Correlation and Scatter Plots
    • 13.2. Simple Linear Regression
    • 13.3. Model Diagnostics and Statistical Inference
    • 13.4. Prediction, Robustness, and Applied Examples
STAT 350: Introduction to Statistics
  • 6. Continuous Distributions
  • View page source

6. Continuous Distributions

  • 6.1. Continuous Random Variables and Probability Density Functions
  • 6.2. Expected Value and Variance of Continuous Random Variables
  • 6.3. Cumulative Distribution Functions
  • 6.4. Normal Distribution
  • 6.5. Uniform Distribution
  • 6.6. Exponential Distribution
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