Dice simulation. The following code computes the exact probability distribution for the sum of two dice:
int[] frequencies = new int[13];for (int i = 1; i <= 6; i++) for (int j = 1; j <= 6; j++) frequencies [i+j]++;double[] probabilities = new double[13];for (int k = 1; k <= 12; k++) probabilities[k] = frequencies[k] / 36.0;
The value probabilities[k] is the probability that the dice sum to k. Run experiments that validate this calculation by simulating n dice throws, keeping track of the frequencies of occurrence of each value when you compute the sum of two uniformly random integers between 1 and 6. How large does n have to be before your empirical results match the exact results to three decimal places?
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