ee3180 bernoulli trial variance calculations

% script file for ee3180 variance calculations for bernoulli trials.  uses
% the function ee3180variance and feeds the parameters p (probability to
% succeed), n (number of trials), and m (number of elements in each trial)
% and returns a vector of the variances of each trial.

% define the 8 cases
fprintf('Bernoulli Trial Variance Calculator\n');
p = input('Define your probability (out of 1): ');
n = input('Define the elements in each trial: ');
m = input('Define the number of trials: ');

variance = ee3180variance(p, n, m);

idealvariance = p * (1 - p) / n;

fprintf('\nThe variance of the mean of these trials is %f,\nand the ideal variance is %f.\n', variance, idealvariance);




function[variance] = ee3180variance(p, n, m)

% step 1:  build the data

for trial = 1:m % there are m trials
    for element = 1:n % there are n elements in each trial
        % set each data(trial, element) to a success (1) or a fail (0)
        if (rand() <= p) % probability p of passing
            data(trial, element) = 1;
        else
            data(trial, element) = 0;
        end
    end
    average(trial) = sum(data(trial, :)) / n;
end

% step 3:  calculate variance of mean

sumofdiffsquared = 0; % init the variable
for trial = 1:m
    sumofdiffsquared = sumofdiffsquared + (average(trial) - mean(average))^2;
end
variance = sumofdiffsquared / (m - 1); % calculate the variance of the mean

end % end the function