Having completed the previous exercises you should be happy that the random numb

Question

Having completed the previous exercises you should be happy that the random number generator in producing a uniform distribution of (pseudo)random numbers. Now we can continue to our first Monte Carlo simulation. Write a program that simulates the outcome of the flipping of an unbiased coin for n flips. Although it will slow the program down significantly, record the ratio of r = number of heats/number of flips for each coin flip. Make a plot of this ratio (as a function of iteration). Run your code for n = 10^1, 10^2, 10^5. Extend your program to consider x coins being flipped simultaneously. Compare your outcome for (n, x) = (10^3, 10) with (n, x) = (10, 1063). Print out your code and an exemplary plot for: (n, x) = (10^3, 100)

Explanation / Answer

NUM_TRIALS = 150;

trials = 1:NUM_TRIALS;

heads = 0;

t = rand(NUM_TRIALS,1);

percent_h=zeros(size(t));

for i = trials

    if (t(i) < 0.5)

        heads = heads + 1;

    end

    percent_h(i) = heads/i;

end

plot(trials,percent_h)

xlabel('Trial Number')

ylabel('Percent Heads')

title ('Trial Number vs Percent Heads')

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