# (Solved Homework): When a fair die is rolled, the number uppermost is equally likely to be any integer betwee…

Matlab

When a fair die is rolled, the number uppermost is equally likely to be any integer between 1 and 6. MATLAB randi function generates uniformly distributed pseudorandom integers. Use this documented MATLAB program (dietoss.m) to simulate a fair die roll of N = 10, 100, 1000 and 10,000 times. For each trial, count the number of sixes thrown by constructing a logical vector and counting the number of times 6 appears. Use MATLAB’s vectorizing commands for logical operators in your solution. Estimate the probability of throwing a six by dividing the number of sixes by 10, 100, 1000 and 10,000 respectively. Compare each to the theoretical expected value of 1/6.

dietoss.m

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th_exp = 1/6.0; %% theoretical exp
N = [ 10,100,1000,10000]; %values of n

for i = 1:4
roll = randi([1,6],N(i),1); % randomly generate rolls in range[1,6]
logical_vector = (roll==6); % calculate logical vector
prob = sum(logical_vector)./N(i); % calculate probility

%display result
fprintf(‘nprobility with %d rolls is %f n’,N(i),prob);
fprintf(‘comparisiion with theortical probablity(%f): %f n’,th_exp,abs(th_exp-prob));
end

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