Elaborating ideas related to probability distributions using software R.

Probability distributions play a major role in science and engineering applications in various domains. Prior knowledge of probability distributions and density functions is mandatory to get deeper insights into any data-driven studies. In undergraduate studies of science and engineering curriculum, these concepts are usually introduced as mathematical functions and their properties are investigated from a purely mathematical perspective. The statistical idea which connects the data to these mathematical functions is often missing. Moreover, handling of real data is challenging at an undergraduate level. In the quest of finding ways to visualize the concepts in a concrete manner, we propose a simulation-based approach to demonstrate different theorems in Statistics. With the growing use of software like R and Python, such experiments can be carried out easily having only minimal programming knowledge. In this poster, I shall utilize the software R to visually aid the concepts related to probability distributions and convergences in probability. The demonstration includes a pictorial understanding of the "Weak Law of Large Numbers" and the "Central Limit Theorem".