Probability & Statistics
181 topics
1Probability & Random Variables
Probability
Combinatorics
Random Variables
- Probability Density Functions of Continuous Random Variables
- Cumulative Distribution Functions for Continuous Random Variables
- Approximating Discrete Random Variables as Continuous
- Median, Quartiles and Percentiles of Continuous Random Variables
- Finding the Mode of a Continuous Random Variable
- Simulating Random Observations
- Calculating Probabilities With Continuous Random Variables
- Continuous Random Variables Over Infinite Domains
2Expectation
Expectation of Random Variables
- Expected Values of Discrete Random Variables
- The Rule of the Lazy Statistician
- Variance of Discrete Random Variables
- Properties of Expectation for Discrete Random Variables
- Moments of Continuous Random Variables
- Variance of Continuous Random Variables
- Properties of Variance for Discrete Random Variables
- Moments of Discrete Random Variables
- Expected Values of Continuous Random Variables
Moment-Generating Functions
- Properties of Moment-Generating Functions
- Calculating Moments Using Moment-Generating Functions
- Constructing Moment-Generating Functions for Discrete Probability Distributions
- The Uniqueness Property of MGFs
- Moment-Generating Functions
- Constructing Moment-Generating Functions for Continuous Probability Distributions
- Calculating Variance and Standard Deviation Using Moment-Generating Functions
3Discrete Probability Distributions
The Binomial Distribution
The Poisson Distribution
The Geometric Distribution
The Discrete Uniform Distribution
The Bernoulli Distribution
4Continuous Probability Distributions
The Normal Distribution
- The Standard Normal Distribution
- The Z-Score
- Modeling With the Normal Distribution
- Mean and Variance of the Normal Distribution
- Normal Approximations of Binomial Distributions
- The Normal Distribution
- The Normal Approximation of the Poisson Distribution
- Percentage Points of the Standard Normal Distribution
- The Empirical Rule for the Normal Distribution
- Symmetry Properties of the Standard Normal Distribution
The Continuous Uniform Distribution
Other Continous Distributions
5Combining Random Variables
Distributions of Two Continuous Random Variables
- The Bivariate Normal Distribution
- Conditional Distributions for Continuous Random Variables
- Joint Distributions for Continuous Random Variables
- Marginal Distributions for Continuous Random Variables
- The Joint CDF of Two Continuous Random Variables
- Independence of Continuous Random Variables
- Properties of the Joint CDF of Two Continuous Random Variables
Distributions of Two Discrete Random Variables
Linear Combinations of Random Variables
Covariance of Random Variables
Expectation for Multivariate Distributions
- Conditional Expectation for Discrete Random Variables
- The Rule of the Lazy Statistician for Two Random Variables
- Variance of Sums of Independent Random Variables
- Expected Values of Sums and Products of Random Variables
- Computing Expected Values From Joint Distributions
- Conditional Variance for Discrete Random Variables
- The Law of Total Expectation for Discrete Random Variables
6Parametric Inference
Maximum Likelihood
- Logarithmic Differentiation
- Maximum Likelihood Estimation
- Product Notation
- Likelihood Functions for Discrete Probability Distributions
- Likelihood Functions for Continuous Probability Distributions
- Log-Likelihood Functions for Discrete Probability Distributions
- Log-Likelihood Functions for Continuous Probability Distributions
The Central Limit Theorem
7Confidence Intervals
One-Sample Procedures
- Confidence Intervals for One Mean: Known Population Variance
- Confidence Intervals for One Variance
- Confidence Intervals for One Proportion
- Confidence Intervals for One Mean: Unknown Population Variance
- Confidence Intervals for One Proportion: Finite Population Corrections
- Confidence Intervals for One Means: Finite Population Correction
Two-Sample Procedures
- Confidence Intervals for Two Means: Known and Unequal Population Variances
- Confidence Intervals for Paired Samples: Known Variances
- Confidence Intervals for Paired Samples: Unknown Variances
- Confidence Intervals for Two Means: Unequal and Unknown Population Variance
- Confidence Intervals for Two Proportions
- Confidence Intervals for Two Means: Equal and Unknown Population Variance
8Hypothesis Testing
One-Sample Procedures
- Introduction to Hypothesis Testing
- Type I and Type II Errors
- Hypothesis Tests for One Mean: Known Population Variance
- Hypothesis Tests for One Mean: Unknown Population Variance
- Hypothesis Tests for One Variance
- Two-Tailed Hypothesis Tests
- Hypothesis Tests for the Rate of a Poisson Distribution
- Critical Regions for Left-Tailed Hypothesis Tests
- Critical Regions for Right-Tailed Hypothesis Tests
Two-Sample Procedures
- Hypothesis Tests for Two Means: Known Population Variances
- Hypothesis Tests for Two Means: Paired-Sample Z-Test
- Hypothesis Tests for Two Means: Equal But Unknown Population Variances
- Hypothesis Tests for Two Variances
- Hypothesis Tests for Two Proportions
- Hypothesis Tests for Two Means: Unequal and Unknown Population Variances
- Hypothesis Tests for Two Means: Paired-Sample T-Test
9Regression
Correlation and Regression
10Nonparametric Inference
Goodness-of-Fit and Order Statistics
- Introduction to Chi-Square Goodness-of-Fit
- Testing Binomial Models Using Chi-Square Goodness-of-Fit
- Testing Poisson Models Using Chi-Square Goodness-of-Fit
- Testing Continuous Uniform Models Using Chi-Square Goodness-of-Fit
- Testing Normal Models Using Chi-Square Goodness-of-Fit
- Chi-Square Tests of Independence and Homogeneity
- Introduction to Order Statistics