Consider a DMS with a two-symbol alphabet source with n = 100 000.
f) Find the mean and variance of Na. Approximate by the central limit theorem approximation. The central limit theorem approximation is to evaluate assuming that Na is Gaussian with the mean and variance of the actual Na.
One point of this exercise is to illustrate that the Chebyshev inequality used in bounding PrT in the text is very weak (although it is a strict bound, whereas the Gaussian approximation here is relatively accurate but not a bound). Another point is to show that n must be very large for the typical set to look typical.