Probability and Statistics

1. Introduction to statistics
1.1. General concepts
1.2. Sampling methods
1.3. Introduction to visualization tools

2. Probability space
2.1. Basic properties
2.2. Independence and conditional probability
2.3. Total probability
2.4. Bayes theorem

3. Univariate statistics
3.1. Visualization techniques
3.2. Characteristic measures
3.3. Transformations

4. Random variables
4.1. Distributions
4.2. Characteristic measures
4.3. Transformations
4.4. Examples

5. Introduction to statistical inference
5.1. Population and sample
5.2. Sampling distribution of a statistic
5.3. The sample mean distribution
5.4. Estimation and estimators
5.5. Method of moments
5.6. Maximum likelihood

6. Confidence intervals
6.1. For the mean
6.2. For the proportion
6.3. For the variance

7. Hypothesis testing
7.1. Introduction to hypothesis testing
7.2. Type I and Type II errors
7.3. Power of a Statistical Test
7.4. p-value

8. Nonparametric goodness-of-fit tests
8.1. Chi-square tests
8.2. Kolmogorov-Smirnov tests