Statistical Analysis: Modelling Random Processes and Data Interpretation

In this module, you will develop a deep understanding of how to model and interpret data arising from random events. You'll explore how simple two-outcome experiments—such as success/failure, yes/no, or defective/non-defective—can be modeled using Bernoulli random variables. Building on this, you will learn to extend these ideas to the binomial distribution, which describes the number of successes in a series of independent trials. This module not only covers the theory behind these distributions but also emphasizes the practical skills needed to compute probabilities, expected values, and variances, and to apply technology in solving real-world problems from fields such as medicine and genetics.

Bernoulli and Binomial Distributions

In this section, you will learn to model situations with two possible outcomes. You will start by understanding Bernoulli random variables, which represent a single trial, and then extend these ideas to the binomial distribution, which counts the number of successes over many trials.

Normal Approximation for the Sample Proportion

This section introduces you to the concept of the sample proportion as a random variable—a critical idea when interpreting data from experiments or surveys. You will explore how, as sample sizes increase, the distribution of the sample proportion becomes approximately normal and how we can use this behaviour to interpret sample data and its limitations

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