Central Limit Theorem - Negative Binomial distribution

Suppose the input data follows the negative binomial distribution with the parameters size = 3 and prob = 0.5. Set the start seed for random numbers as 1234.

a) Generate 1000 random values from this distribution. Show the barplot with the proportions of the distinct values of this distribution.

b) With samples sizes of 10, 20, 30, and 40, draw 5000 samples from the data generated in (a). Use sample() function with replace as FALSE. Show the histograms of the densities of the sample means. Use a 2 x 2 layout.

c) Compare of means and standard deviations of the data from a) with the four sequences generated in b).