Iteration of increasing number of random numbers

Questions
1

Consider the following code:

n = 10;
    t = Table[RandomInteger[], n];
    c = Counts[t]
    c1 = c[[1]] - n/2
    avg = c1/n // N

Basically I would like to produce a graph showing how increasing the number of trials causes the result to trend towards zero. I would like to iterate the above formulas over {n^i, {i,0,10}} and then graph the avg so the different number of trails can be compared, for n = 10, 100, 1000, etc. But I have a problem with c[[1]] takes the first position in the list and the first position is sometimes 0 and sometimes 1 and I would like to just look at “1”.

2

So you are just interested in the number of times 1 appears in the list, right? There are several ways to do this. Here are a couple.

Reverse sort the counts:

c = Counts[t] // KeySortBy[Minus]

Filter out the zero’s before counting:

t = Table[RandomInteger[], n] // Select[# > 0 &]
3

thanks Rohit, that is a start

n = 10;
t2 = Counts[Table[RandomInteger[], n] // Select[# > 0 &]];
(t2[[1]] - n/2)/n // N

now I would like to repeat this process to create a list where n increases, something like the following but it doesn’t work

Table[
 t2 = Counts[Table[RandomInteger[], n] // Select[# > 0 &]];
 (t2[[1]] - n/2)/n // N, n = 10^i, {i, 0, 10}]
4

n needs to be defined before it is used.

Table[n = 10^i; 
 t2 = Counts[Table[RandomInteger[], n] // Select[# > 0 &]];
 (t2[[1]] - n/2)/n // N, {i, 1, 6}]

Starting i at 0 means there is a 50% chance that the count of 1 is 0 so Counts will return an empty Association and Part will fail. Also, ending it at 10 means the table will have 10^10 values.

5

Rohit, thank you very much for giving insight into my mistakes