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**acevipa** Show that the following functions are probability densities, i.e.

$\displaystyle f(x)\geq 0$ and $\displaystyle \int_{-\infty}^{\infty}f(x) dx =1$

Uniform distribution:

$\displaystyle f(x)=\left\{\begin{array}{cc}\frac{1}{b-a} & \mbox{ for } a\leq x \leq b\\0 & \mbox{ otherwise }\end{array}\right.$

Pareto distribution: For $\displaystyle k>0$

$\displaystyle f(x)=\left\{\begin{array}{cc}\frac{k}{x^{k+1}} & \mbox{ for } x \geq 1\\0 & \mbox{ otherwise }\end{array}\right.$