Probability and Statistical Distributions

In this course, students will understand the fundamentals of probability, including the concept of sample space and the three main approaches — classical, frequentist, and subjective — for quantifying uncertainty in random phenomena. Discrete probability distributions such as Binomial and Poisson, and continuous distributions, will be explored, highlighting the Normal, Uniform, and Exponential distributions, essential for modeling variable behavior and predicting outcomes.

The module also covers fundamental statistical measures, such as expected value, variance, and standard deviation, which summarize the behavior of distributions and aid in interpreting data. Statistical inference is introduced through the Central Limit Theorem, confidence intervals, and hypothesis tests, allowing information to be extrapolated from samples to entire populations with analytical rigor and uncertainty control.

Finally, students will study practical applications of probability and statistics in real-world contexts, including industrial quality control, consumer behavior research, finance, and public health. Modern computational tools will be highlighted, such as Excel, R, and Python, to speed up calculations, generate visualizations, and support data-driven strategic decision-making.