The goal of this milestone is to demonstrate data loading, cleaning, and basic exploratory analysis in preparation for building a predictive text algorithm. This report provides a clear overview of the dataset, identifies common words and phrases, and sets the stage for model development.

This R script is a hands-on guide to the Moment Generating Function (MGF) of the Discrete Uniform Distribution. It defines a custom function, uniform_mgf, to calculate the MGF for any discrete uniform random variable. The code then uses this function to demonstrate a powerful application: approximating the distribution's mean and variance by taking numerical derivatives of the MGF evaluated at t=0. The script also provides two informative plots to visualize these concepts. The first plot displays the MGF for different distributions (e.g., a 6-sided die, a 10-sided die, etc.), showing how the function's curve changes with the number of possible outcomes. The second plot illustrates the fundamental relationship between the number of outcomes and the key moments of the distribution, clearly showing that the mean grows linearly, while the variance increases quadratically. This visualization effectively reinforces the theoretical properties of the discrete uniform distribution discussed in the blog post.

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