For python:

1. Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score".
2. Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean 1 and standard deviation 1 of this distribution. Compare your numerical result to the analytical calculation.
3. Generate 1000 sets of throws of N=2,3,4,5,10 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean N and standard deviation N of each distribution. This should be similar to the plot at the link above.
4. Plot the standard deviation N as a function of N. Does it follow the Central Limit Theorem?