I believe that calling out certain points in the video “Central Limit Theorem - Discrete Random Variable” would make it easier to understand.
At the beginning of the video Luis introduces the concept by saying, “Take a distribution… take a few samples… look at the average, and do this many times and plot all these averages… you get the normal distribution no matter what distribution you started with in the first place.” However, the subsequent example in the video actually focuses on the sum instead of the average. While it is evident that the sum will follow a normal distribution if the mean does, it would be clearer to explicitly mention this in the video for educational purposes.
Furthermore, to enhance understanding, it would be beneficial to include a statement similar to the following when illustrating the example of tossing coins in the video, in order to establish a connection between the example and the introductory explanation of the theorem: “The original distribution is a Bernoulli distribution. Every time we draw ‘n’ values (0/1, where 1 denotes heads and 0 denotes tails) from this distribution—essentially, tossing ‘n’ coins—and calculate the sum. The probability distribution of the sum approaches a normal distribution as ‘n’ increases.”
Currently, the illustration in the video does not explicitly mention the Bernoulli distribution, which might cause learners to think about a binomial distribution. I reckon It is crucial to explicitly mention the Bernoulli distribution to help learners understand that each time we draw ‘n’ values from a Bernoulli distribution and do the sum.