Question: A continuous random variable X has a Pareto distribution if its probability density function has the form where a and are parameters (positive real

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

f(x)= = xa+1 0 if x = x otherwise

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).

f(x)= = xa+1 0 if x = x otherwise

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