Illustrating the central limit theorem

Question

I'm working on this question is from Wolfram Mathematica online course. I tried my best to find the answer, still not getting it right

The question is:

Make a list of histograms of 10000 instances of totals of n random reals up to 100, with n going from 1 to 5 (illustrating the central limit theorem)

The Central limit theorem states that (From Wikipedia)

In probability theory, the central limit theorem (CLT) establishes that, in many situations, for identically distributed independent samples, the standardized sample mean tends towards the standard normal distribution even if the original variables themselves are not normally distributed.

I have tried this

Table[Histogram[RandomReal[n*100, 10000]], {n, 5}]

But one would expect the Histogram become more of a Gaussian.

Answer 1

You need to generate 10000 sums of n random numbers and make a histogram of these sums. In your code you just sum up 10000 uniformly distributed random numbers 5 times.

With the corrected code below you can see that for increasing n the distribution approaches the normal distribution as stated by the central limit theorem.

Table[
    Histogram[
        Table[
            Total[
                RandomReal[100, n] (* generate n random numbers in the interval [0, 100] *)
            ] (* sum these n numbers *)
        , 10000] (* do this 10000 times *)
    ] (* make a historgram of these 10000 summed values *)
, {n, 1, 5}] (* generate histograms with n in {1, 2, 3, 4, 5} *)

PS: A very illustrative post about the central limit theorem can also be found over on stackoverflow.