Question

A perfect coin should produce heads and tails with equal probability. If we assign the number 0 toheads and the number 1 to tails, then we can mimic such a perfect coin in Matlab. Specifically, we cangenerate N “coin flips” in Matlab by doing x= (rand(N, 1) < 0.5 );, where becomes an array of zeros(“heads") and ones (“tails"). For a perfect coin, the mean of that array should be exactly 0.5. Experimentwith how many coin flips you need to get close to this value. Specifically, generate N = 16 coin flips and compute the sample mean (in Matlab, mean(x)). Then generate N = 32 coin flips and compute a newmean. Repeat this process for N = 2k for k = 4,5,…,26. For each value of N, the error in your computedmean is the absolute value of the computed sample mean and 0.5 (i.e., error = abs( mean(x) - 0.5 );). Plot this error vs N. Try linear and logarithmic axes. What patterns do you see?

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