Exercise Solution 3.45

  1. The following exhibit illustrates PDFs of  for n equal to 1 through 5.

    For n = 3, the distribution already has the “bell” shape of a normal distribution, although its tails are modest. For n = 4 or n = 5, the PDFs could be mistaken for the standard normal PDF.

  2. A normal distribution has a kurtosis of exactly 3. The following exhibit lists the kurtoses of  for n = 1 through n= 40. All values are rounded to four decimal places. If we round to a single decimal place, the first kurtosis that equals 3.0 is for n = 24.