## Introduction to Statistics and Probability

Much of the material that is currently on this blog is going to be moved to https://mathsatstatslab.wordpress.com/ very soon.

**1. Introduction to Statistics**

- Types of data
- Variables (Notes)

**2. Introduction to Probability**

- Sample Spaces
- Basic Probability Distribution
- Rules of Probability
- Independent Events
- Conditional Probability [6:45]
- The Addition Rule for Probability
- Probability Trees (Example 1)
- Probability Trees (Example 2)

**3. Techniques for Counting**

- Venn Diagrams
- Sampling with/out Replacement
- Choose Operator (Binomial Coefficients)
- Choose Operator Exercises [9:16]
- Permutations

**4. Descriptive Statistics**

- Measures of Centrality
- Computing the Median of a Data Set.
- Introduction to Dispersion
- Measures of Dispersion
- Box plots (Box and Whisker Plots)
- Five Number summary, IQR, Fences, Midhinge and Trimean [6:51]

**5. Random Variables**

- Introduction to Probability Distributions
- Expected Values and Probability
- Joint and Marginal Distributions
- Probability Mass functions

**6. Discrete Probability Distributions**

- The binomial distribution
- The geometric distribution
- The Poisson distribution

**7. Continuous Probability Distributions**

- Interval Probabilities for Continuous Random Variables.
- The Uniform distribution
- Exponential Distribution [15:00]
- Other important Continous probability distributions (Notes)

**8. Normal Distribution**

- Standardization and Z-scores
- Using Statistical Tables
- The Complement and Symmetry Rules
- Interval Probability (example)
- Asssumption of Normality (Notes)

**9. Introduction to Statistical Inference**

- Sampling (Notes)
- Sampling Distributions and the Central Limit Theorem
- Standard Error for the Mean
- Introduction to Confidence Intervals (Notes)
- Hypothesis testing
- Type I and II Error (Notes)

**9A. Commonly used Hypothesis Tests**

- Hypothesis test for the mean of a single sample
- Hypothesis test for the mean of two independent samples
- Hypothesis test for the proportion of a single group
- Hypothesis test for the proportions of two independent samples
- Other Inference Procedures

**10. Statistical Procedures for simple samples**

- One-tailed tests for means
- Confidence Intervals for Proportions

**11. Statistical Procedures for two indepedent samples**

- Assumption of Equal Variance (The F-test)

**12. Non-Parametric Statistics**

- Introduction to Non-Parametric Statistics (Notes)
- Non-Parametric Statistical Measures

**13. Goodness of Fit tests**

- Chi-Square Univariate Test
- Chi-Square Goodness of Test

**14 Bivariate Data**

- Correlation
- Spearman’s Correlation (notes)
- Simple Linear Regression

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