A continuous random variable X has a Pareto distribution if its probability density function has the form

where a and λ are parameters (positive real numbers). The Pareto distribution is often used to model the distribution of incomes in a society. Exercises 56 and 57 involve the Pareto distribution.

Suppose X is a random variable that has a Pareto distribution with parameter a = 1 and λ = 1.2.

a. Sketch the graph of the probability density function f(x) for X.

b. Find the probability P(10 ≤ X ≤ 20).

Transcribed Image Text:

f(x)= = αλα xa+1 0 if x = x otherwise