The probability density function relating to the number of seconds that individuals remain on a website until they leave is given by the Pareto distribution,

\(f(x)=\left(\begin{array}{c}\frac{\alpha \beta^{\alpha}}{x^{\alpha+1}} \\ 0\end{array}ight)\) for \(x\left\{\begin{array}{l}> \\ \leq\end{array}ight\} \beta, \alpha=2\) and \(\beta=5\).

(a) Simulate observations on the number of seconds that each of 25 visitors spends visiting the website.

(b) Calculate the sample mean and variance. Compare them to the true mean and variance, if they exist.