Central Limit Theorem: Verification using Exponential Distribution with mu = 5

This script is to verify the Central Limit Theorem in probability theory or statistics. The Central Limit Theorem states that, regardless of the distribution of the population, the sampling distribution of the sample means, assuming all samples are identical in size, will approach a normal distribution when the sample size is getting larger, e..g., sample size is greater than to equal to 30. This video is to verify the above statement by running a simulation. The population follows an exponential distribution (with mu = 5). The video is to show the evolution of the histogram by adding more and more samples in each time step. Label the sub-figures shown in the video as below: ------------- | 1 | 2 | 3 | ------------- | 4 | 5 | 6 | ------------- The top left figure in the video, e.g., Fig. 1, show the histogram of the samples drawn from an exponential distribution (with mu = 5) that the x-axis is sample's value and the y-axis is the number of occurrences of the sample's values. Figs 2 to 5 show the histograms (sampling distributions) of the means of the samples drawn from an exponential distribution (with mu = 5). The number of samples drawn are 2, 5, 10, 30, 100, respectively, in Figs. 2 to 5. The figures shows that, when sample sizes are 30 and 100, the sample distributions approximate a normal distribution.