Question: A fair, six-sided die is rolled t times. (a) Let t = 6n and compute pt (n), the probability that all six sides occur

A fair, six-sided die is rolled t times.

(a) Let t = 6n and compute pt (n), the probability that all six sides occur exactly n times. Approximate the result using Stirling’s approximation n! ≈

(2π)

1/2 nn+1/2e−n from (1.42) and compute the associated relative percentage error for n = 1, 2, ... , 20.

(b) For general t, compute the probability pt that all six sides occur at least three times. Construct a program which computes pt and also simulates the result. Plot the exact pt versus t = 18, 20, ... , 60 along with the simulated results for several values of t.

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