Introduction
- What is statistics ?
- The statistical process
- Population and samples
- Random sampling
Descriptive Statistics
- Introduction
- Types of variables
- Graphical representations
- Descriptive measures
Elements of Probability
- Events
- Probabilities
- Conditional Probabilities
- Independent Events
- Bayes’ Formula
Random variables
- Random variables
- Discrete Random Variables
- Continuous Random Variables
- Expectation of a random variable
- Variance of a random variable
- Jointly distributed Random Variables
Special random variables
- Binomial random variables
- Hypergeometric random variables
- Poisson random variables
- Uniform random variables
- Exponential random variables
- Normal random variables
- Checking if the data are normally distributed
- Normal random variables
- Checking if the data are normally distributed
Interval estimation
- Interval estimation
- Confidence interval on the mean of a normal distribution, variance known
- Confidence interval on the mean of a normal distribution, variance unknown
- The Student’s t-distribution
- General method to derive a confidence interval
- Central Limit Theorem
- Confidence interval on the mean of an arbitrary population
- Prediction intervals
Point estimators
- Introduction
- Estimation and sampling distribution
- Point estimation
- Properties of estimators
Sufficient Statistics
- Introduction
- Factorization Theorem
The likelihood and conditionality principles
- The conditionality principle
- The likelihood principle
Bayesian Inference
- Introduction
- Bayesian statistical model
- Decision theory
- Bayesian Vs. Frequentist
- Loss functions
- How to Choose Priors
- From theory to practice
- Conjugate priors
Hypothests Testing
- Tests of Hypotheses
- Confidence Intervals vs. Hypothesis Tests
- Likelihood Ratio Test
- Bayes’ criterion
- Minimax criterion
- Neyman-Pearson criterion
- Uniformly most powerful test
Regression Analysis
- Simple Linear Regression
- Least Squares Estimators
- Inferences in simple linear regression
- Adequacy of the regression model
- Correlation