PDFs for two continuous random variables are illustrated in Exhibit 3.4. Assume probability density is 0 for both distributions outside the graphed regions. Where possible, indicate which random variable has the greater:

a. expectation,

b. standard deviation,

c. skewness,

d. kurtosis, and

e. .25-quantile.

a. The distribution on the right has the greater expectation.

b. It is impossible to tell which distribution has the greater standard deviation.

c. The distribution on the left has positive skewness. The distribution on the right appears symmetric, so it has zero skewness.

d. The distribution on the left is more peaked and has fatter tails, so it has greater kurtosis.

e. The distribution on the right has the greater .25-quantile.