i have to plot the percentage of heads by the times token is trowed times, in a game of head or tail, but a need help for doing that. What can I use in my plot?

------- the token is throwed n times, and I also need to know how to add a line at 50 percent at my plot

N = input('Coloque um valor para N: ');

cara = 0;
coroa = 0;

x=rand(1,N);

for i = 1:length(x)
    if x(i) < 0.5
        x(i) = 0; % cara

    else 
        x(i) = 1; % coroa
    end
end

figure
histogram(x);
title('Gráfico')

for i = 1: length(x)
    if x(i) == 0
        cara = cara + 1;
    else
        coroa = coroa + 1;
    end
end

plot(cumsum(x==0))

Answer 1

[Torsten]

N = 500;
x=rand(1,N);
for i = 1:length(x)
    if x(i) < 0.5
        x(i) = 1; % cara
    else 
        x(i) = 0; % coroa
    end
end
plot((1:N),100*cumsum(x)./(1:N))

[Image Analyst]

@LUIS Clarification note: at the end, this will give you the probability for one experiment of tossing it 500 times. It does not give you the probability as a function of N (my code doesn't either) where N varies. If that's what you want, that's fine. And if the N is small, like 20, you can see from this one experiment's plot, it might give a probability of 30% instead of 50%. That's why I said to toss it 20 times like a million times - to get the true probability for 20 which should be 50%. But if what you want is to see the fraction as it approaches 50% as the number of tosses increases, then this shows it to you. Just be aware that the count for a certain number of tosses is not the probability for that number of tosses.

If you want a probability for all N, you'd need another, outer loop to have N vary.

for N = 2 : 500

instead of having N be fixed at some number like 20 or 500. So in essence you'd be building up an array giving the final value only of the plot above as N increases.

Answer 2

[Image Analyst]

You need a nested for loop. The inner loop will throw the token/coin N (or n) times and give you a percentage for that one experiment. Now you need to do that experiment a lot of times, like a million times or so, and that will be the outer loop

numExperiments = 1000000;
numTossesPerExperiment = N;
for k1 = 1 : numExperiments
    countsThisExperiment = 0; % Reset counter.
    % Toss coin N times counting the number of heads.
    for k2 = 1 : N
        % to do
    end
    % Record the percentage for this experiment
    counts(k1) = nnz(x) / N;
end
histogram(counts);
grid on;

Answer 3

[Voss]

% N = input('Coloque um valor para N: ');
N = 2500;
x = round(rand(1,N));

figure
histogram(x);
title('Total #')
xticks([0 1])
xticklabels({'cara','coroa'})

figure()
plot(cumsum(x==0))
title('# of cara vs # of throws')
xlabel('throws')
ylabel('cara')

figure
plot(cumsum(x==0)./(1:N))
hold on
plot([1 N],[0.5 0.5],'--r')
title('proportion of cara')
xlabel('throw #')