### My learning journey in Fundamentals of Statistics

My learning journey in Fundamentals of Statistics has been an enlightening experience that has provided me with a strong foundation in statistical concepts and techniques. Throughout my journey, I gained knowledge of various statistical methods and learned how to apply them to real-world problems.

At the beginning of my journey, I started by learning the basics of statistical analysis, including descriptive statistics, probability theory, and inferential statistics. I also learned how to use statistical software such as R and Excel to perform data analysis and generate visualizations.

As I progressed further, I began to explore different statistical methods and techniques used in research. I learned about regression analysis, hypothesis testing, ANOVA, and other multivariate techniques. I also gained knowledge of different study designs, such as experimental and observational studies, and how to analyze and interpret data from these designs.

One of the most valuable lessons I learned during my journey was the importance of interpreting and communicating statistical results. I learned how to write clear and concise reports and how to effectively communicate statistical results to a non-technical audience.

Finally, I had the opportunity to apply my knowledge and skills in a real-world setting, through various projects and research studies. This allowed me to gain practical experience in analyzing and interpreting data, and provided me with insights into the challenges and complexities of data analysis.

**Week 1: Probability and Linear algebra Review**

- Probability Theory: The course provides a review of probability theory, including the definition of probability, sample spaces, events, and probability axioms. The module also covers important probability distributions such as the binomial, Poisson, and normal distributions, and discusses the central limit theorem.
- Linear Algebra: The module covers the basics of linear algebra, including vectors, matrices, and linear transformations. It covers operations such as addition, subtraction, scalar multiplication, and matrix multiplication. The module also covers matrix inverses, determinants, and eigenvectors, and their applications in data analysis.
- Applications in Statistics: The module shows how probability and linear algebra are used in statistical analysis, such as in regression analysis and hypothesis testing. The module highlights the importance of understanding these concepts to perform advanced statistical analysis and to interpret statistical results. The module also covers the use of statistical software such as R and Excel to perform data analysis and generate visualizations.

I found some problems quite interesting:

**Discrete random variables**

Normalization constant for the Poisson distribution

The probability mass function (pmf) of a **Poisson distribution** with parameter lamda is given by:

**Week 2: Introduction to Fundamentals of Statistics**

- Definition of Statistics: The course provides an overview of statistics and its applications in various fields such as medicine, engineering, and social sciences. The module covers the definition of statistics, its scope, and the role of statistics in decision making.
- Data Types and Measurement: The course introduces different types of data, such as nominal, ordinal, interval, and ratio data, and the different scales of measurement used to classify them. The module also covers methods for collecting data, including surveys, experiments, and observational studies.
- Descriptive Statistics: The module covers descriptive statistics, including measures of central tendency (mean, median, mode) and measures of variability (range, variance, standard deviation). It also introduces graphical techniques for summarizing data, such as histograms, box plots, and scatter plots. The module highlights the importance of descriptive statistics in summarizing and interpreting data, and how they can be used to communicate results effectively.

I found some problems quite interesting:

**Population versus samples**

**Week 3: Foundation of Inference**

- Estimation: The course covers point estimation and interval estimation, including maximum likelihood estimation, the method of moments, and confidence intervals. The module also covers the properties of estimators, such as unbiasedness, consistency, and efficiency.
- Hypothesis Testing: The module covers the basics of hypothesis testing, including the null and alternative hypotheses, the level of significance, and the test statistic. The module also covers different types of tests, such as the t-test, z-test, and chi-square test, and discusses the p-value and its interpretation.
- Linear Regression: The module covers simple linear regression and multiple linear regression, including the estimation of regression coefficients, the interpretation of regression output, and the use of regression analysis in predicting outcomes. The module also covers assumptions of linear regression, such as linearity, independence, and normality, and discusses how to test these assumptions. The module highlights the importance of regression analysis in data analysis and its use in various fields, such as economics, social sciences, and engineering.

I found some problems quite interesting:

**Biased and unbiased estimation for variance of Bernoulli variables**

Let X1 … Xn be i.i.d. Bernoulli random variables, with unknown parameter p is belonging to (0,1). The aim of this exercise is to estimate the common variance of the Xi.

First, recall what Var(Xi) is for Bernoulli random variables.

Overall, my learning journey in Fundamentals of Statistics has been an enriching experience that has equipped me with the necessary knowledge and skills to analyze and interpret complex data. I look forward to applying these skills in my future research and contributing to the continued advancement of statistical analysis.

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