Welcome to the ultimate guide on leveraging Python for statistics and probability!
This repository is packed with resources and chapters designed to take your statistical knowledge to new heights. Whether you’re a beginner wanting to grasp the basics or a seasoned pro aiming to polish your skills, you will find invaluable insights here.

Table of Content

• Chapter 1: Special Continuous Random Variables
• 1.1. Normal (Gaussian) Distribution
• 1.2. Chi-square Distribution
• 1.3. T-student Distribution
• 1.4. Fisher Distribution
• 1.5. Continuous Uniform Distribution
• 1.6. Exponential Distribution
• 1.7. Gamma Distribution
• 1.8. Beta Distribution
• 1.9. Weibull Distribution
• 1.10. Cauchy Distribution
• 1.11. Laplace Distribution
• 1.12. Logistic Distribution
• Chapter 2: Special Discrete Random Variables
• 2.1. Bernoulli Distribution
• 2.2. Binomial Distribution
• 2.3. Negative Binomial (Pascal) Distribution
• 2.4. Geometric Distribution
• 2.5. Poisson Distribution
• 2.6. Discrete Uniform Distribution
• 2.7. Hypergeometric Distribution
• Chapter 3: Confidence Intervals
• 3.1. Confidence Interval for the Mean of a Normal Population
• 3.2. Confidence Interval for the Variance of a Normal Population
• 3.3. Confidence Interval for the Difference in Means of Two Normal Populations
• 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
• 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable
• Chapter 4: Parametric Hypothesis Testing
• 4.1. Introduction
• 4.2. Test Concerning the Mean of a Normal Population
• 4.3. Test Concerning the Equality of Means of Two Normal Populations
• 4.4. Paired t-test
• 4.5. Test Concerning the Variance of a Normal Population
• 4.6. Test Concerning the Equality of Variances of Two Normal Populations
• 4.7. Test Concerning P in Bernoulli Populations
• 4.8. Test Concerning the Equality of P in Two Bernoulli Populations
• Chapter 5: Statistical Hypothesis Testing
• 5.1. Normality Tests
• 5.2. Correlation Tests
• 5.3. Stationary Tests
• 5.4. Other Tests
• Chapter 6: Regression
• 6.1. Introduction
• 6.2. Least Squares Estimators of the Regression Parameters
• 6.3. Statistical Inferences about the Regression Parameters
• 6.4. Confidence Intervals Concerning Regression Models
• 6.5. Residuals
• Chapter 7: Analysis of Variance (ANOVA)
• 7.1. One-Way Analysis of Variance
• 7.2. Two-Way Analysis of Variance

Getting Started

To get started with the statistics and probability concepts in this repository, you can follow the links in the Table of Content above. Each chapter is designed with simplicity in mind, integrating practical examples using Python for hands-on learning.

Understanding the Core Concepts

Think of statistical distributions as different flavors of ice cream. Each flavor has its own unique taste and texture based on the ingredients (i.e., data) used to create it. For example, the Normal distribution, resembling classic vanilla, is commonly used, whereas the Chi-square distribution, with its unique zest, has specific applications in hypothesis testing. Just like choosing an ice cream flavor that matches your mood, picking the right distribution requires understanding its properties and when to use it.

Troubleshooting

While delving into statistics with Python, you may encounter some common issues. Here are a few troubleshooting ideas:

• Error in Importing Libraries: Ensure that you have installed all necessary libraries. Common tools include NumPy, SciPy, and Matplotlib. Use the command `pip install numpy scipy matplotlib` if needed.
• Data Type Issues: If an error arises related to data types, make sure that your data is in a numpy array or pandas DataFrame.
• Function Not Found: If you come across a ‘function not found’ error, double-check the spelling and make sure the function is part of an installed library.
• Unexpected Results: Always visualize your data first. Graphical representations can often illuminate issues or assumptions in your data that might lead to unexpected results.

For more insights, updates, or to collaborate on AI development projects, stay connected with fxis.ai.

Conclusion

At fxis.ai, we believe that such advancements are crucial for the future of AI, as they enable more comprehensive and effective solutions.
Our team is continually exploring new methodologies to push the envelope in artificial intelligence, ensuring that our clients benefit from the latest technological innovations.

Happy coding and statistical analysis!