Variable simulation not being able to be graphed.

I was working on some piece of code that simulates the birthday paradox based on the user selected sample size and the number of realizations that the user wants. I'm a little bit confused as the variable 'Simulation' only produces one probablity value not a array of probablity values. Therefore the exponential graph can't be sketched.

Here's the code:

disp('Welcome to the Birtday Paradox')
ready = false;
while ~ ready
    % User inputs and defining variables
    birthday_repeats = input('select the number of birthday repeats from 10-500:');
        if birthday_repeats > 500 || birthday_repeats < 10 || isempty(birthday_repeats) || round(birthday_repeats) ~= birthday_repeats|| isnan(birthday_repeats)
            disp('error')
            continue
        end
    sample_size = input('Select the sample size from 2-365: ');
        if sample_size > 365 || sample_size < 2|| isempty(sample_size) || round(sample_size) ~= sample_size || isnan(sample_size)
            disp('error')
            continue
        end
   N = 1000;
   days = randi(365,1,365);
   tally = zeros(1,sample_size);
   % simulation run
   for k = 2:sample_size
       match = 0;
       for j = 1:birthday_repeats% desired number of trials
            birthdays = randi(365,1,k);
            if test(days)
                match = k + 1;
            end
       end
    Simulation = tally(k) - match/birthday_repeats;
   end
   
    % plotting graphs
    domain = 2:sample_size;
    figure(1)
    plot(domain,Simulation)
    xlabel('Number of people Chosen')
    title('Birthday Paradox simulation')
    ylabel('Probability')
    fprintf('the probablity is %.3f\n',Simulation)
    break
end

Here's the code for the user defined function 'test'

function out = test(data)
out = false;
n = length(data);
for k = 1:n
    for i = k+1:n
        if data(k) == data(i)
            out = true;
            return
        end
    end
 end
end

Answer 1

[LeoAiE]

The main change I made was to update the tally(k) value inside the for loop instead of assigning it at the end. This way, the tally array is populated with the probability values for each sample size.

disp('Welcome to the Birtday Paradox');
ready = false;
while ~ ready
    % User inputs and defining variables
    birthday_repeats = input('select the number of birthday repeats from 10-500:');
        if birthday_repeats > 500 || birthday_repeats < 10 || isempty(birthday_repeats) || round(birthday_repeats) ~= birthday_repeats || isnan(birthday_repeats)
            disp('error')
            continue
        end
    sample_size = input('Select the sample size from 2-365: ');
        if sample_size > 365 || sample_size < 2|| isempty(sample_size) || round(sample_size) ~= sample_size || isnan(sample_size)
            disp('error')
            continue
        end
    N = 1000;
    days = randi(365,1,365);
    tally = zeros(1,sample_size);
    % simulation run
    for k = 2:sample_size
        match = 0;
        for j = 1:birthday_repeats % desired number of trials
            birthdays = randi(365,1,k);
            if test(birthdays)
                match = match + 1;
            end
        end
        tally(k) = match/birthday_repeats;
    end
    % plotting graphs
    domain = 2:sample_size;
    figure(1)
    plot(domain,tally(2:end))
    xlabel('Number of people Chosen')
    title('Birthday Paradox simulation')
    ylabel('Probability')
    fprintf('the probability array is:\n');
    disp(tally(2:end))
    break
end

function out = test(data)
    out = false;
    n = length(data);
    for k = 1:n
        for i = k+1:n
            if data(k) == data(i)
                out = true;
                return
            end
        end
    end
end

[Kiran Sai]

Is it supposed to give a linear graph as an output?

Answer 2

[Walter Roberson]

    Simulation = tally(k) - match/birthday_repeats;

tally(k) is a scalar. So are match and birthday_repeats. So the right hand side of the assignment is a scalar, and that means that the output will be a scalar -- not something that is the same size as 2:sample_size

[Kiran Sai]

Is there a way to convert the scald into a array?

[Walter Roberson]

Sure. Assign to Simulation(k-1) instead of to the entire array Simulation

The -1 part is because k starts at 2 not at 1, and when you use Simulation later, you are not indexing it -- so the first output of Simulation (offset 1) has to correspond to k = 2.