The extent to which a distribution is peaked or flat also

Question

The extent to which a distribution is peaked or flat, also called the kurtosis of the distribution, is often measured by means of the quantity

Use the formula for μ₄ obtained in Exercise 25 to find α₄ for each of the following symmetrical distributions, of which the first is more peaked (narrow humped) than the second:

Exercise 25

Show that

for r = 1, 2, 3, ... , and use this formula to express μ₃ and μ₄ in terms of moments about the origin.