Central Limit Theorem Illustrative Movie

Frames comparing sample mean distribution A_k to approximate normal distribution as k goes from 1 to n.

User can input

• a specific distribution X or set to random.
• max sample size n
• number of samples ns

Output is a movie or a single image.

• Movie: The k-th frame shows the histogram of ns many sample means of sample size k, showing the shape of A_k = (X_1 + X_2 + ... + X_k) / k, and the approximate normal distribution given by the central limit theorem.
• Single Image: Only the final frame of the movie is shown.

Purpose: This is intended for education, e.g., an instructor can demonstrate the limiting process of the central limit theorem for a variety of distributions. Also, the code is intended for students with no programming background in that inputs are found within the code and line numbers of said inputs are given in the preamble.