Final answer:
A random variable X following a Pareto distribution with shape parameter γ has a probability density function (PDF), where x ≥ k (the scale parameter). The distribution is continuous with X ranging from k to positive infinity.
Step-by-step explanation:
Calculating the PDF of a Pareto Distribution
The Pareto distribution is a continuous probability distribution named after the economist Vilfredo Pareto. It is often used in descriptions of social, scientific, geophysical, actuarial, and many other types of observable phenomena. A random variable X following a Pareto(γ) distribution, where γ is a positive parameter (shape parameter), has a probability density function (PDF) given by:
f(x;γ) = γ * k^γ / x^(γ+1), for x ≥ k
and 0 otherwise
where k is the scale parameter and it is the minimum possible value of X. The shape parameter γ determines the ‘tail’ of the distribution.
Range of Possible Values for Pareto Distribution
The Pareto distribution is continuous and is defined for X ≥ k. There is no upper limit to the values that X can take. Practically, this means that X can range from the scale parameter k to positive infinity.