Question: An alternative to the lognormal distribution for modeling highly skewed populations is the Pareto distribution with parameters Î¸ and r. The probability density function is

An alternative to the lognormal distribution for modeling highly skewed populations is the Pareto distribution with parameters Î¸ and r. The probability density function is f(x) = { xr+l

The parameters Î¸ and r may be any positive numbers. Let X be a random variable with this distribution.

a. Find the cumulative distribution function of X.

b. Assume r > 1. Find Î¼_X.

c. Assume r > 2. Find Ïƒ²_X.

d. Show that if r ‰¤ 1, Î¼_X does not exist.

e. Show that if r ‰¤ 2, Ïƒ²_X does not exist.

f(x) = { xr+l

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