(Solved): The Pareto distribution function has a probability density as shown below with the shape parameter ...

The Pareto distribution function has a probability density as shown below with the shape parameter ? and the scale parameter ?.

\[ \frac{\alpha \beta^{\alpha}}{x^{\alpha+1}} \text { for } x>\beta \] (a) Find the cumulative density function \( \mathrm{F}(\mathrm{x}) \) (b) Write an algorithm using the CDF inverse method to generate random numbers from \( \operatorname{Pareto}(\alpha=20, \beta=3) \) (c) Write \( \mathrm{R} \) code to generate 10,000 random numbers and draw a EDF plot.