Attribute | Rank |
---|---|

Difficulty | 3 |

Proof Quality | 4 |

Readability | 4 |

Self-Study | 4 |

Good for Teaching? | 5 |

Quality of Exercises | 5 |

- Basic probability
- Conditional probability, independence
- discrete and continuous random variables, various distributions
- expectation of random variables
- important inequalities (e.g. Chebyshev's inequality)

- Multivarite Distributions
- Bivariate distributions, marginal distributions, conditional distributions
- correlation coefficient

- Special Distributions
- Binomial, Multinomial
- Poisson
- $\Gamma, \chi^{2}, \beta$ distributions
- Normal and multivariate normal
- t and F distributions

- Consistency, Bias, and Limiting Distributions
- Convergence in probability and distribution
- central limit theorem

- Elementary Statistical Inference
- Order statistics
- confidence intervals
- hypothesis testing
- Chi-Square tests
- Monte-Carlo methods
- Bootstrapping

- Maximum Likelihood Methods
- Sufficient Statistics
- Optimal Hypothesis Testing
- Inference on Normal Models
- One-way ANOVA
- noncentral $\chi^{2}$ and F distributions
- Multiple comparisons

- Nonparametric Statistics
- Sign test
- Signed-Rank Wilcoxon test
- Mann-Whitney-Wilcoxon procedure
- general rank tests
- nonparametric measures of association

- Bayesian Statistics
- Linear Models
- Robustness