Since this is a Pareto distribution:

1. The support is . So you need to show that .

(*Ahem .... note what is in red by the way).

2. You should realise that and . Knowing is of particular importance in solving the integral.

Now you should note that .

So you have a simple improper integral to calculate.

--------------------------------------------------------------------------------------------------------------------------

As for the variance, you should know that . So set up the necessary integrals and calculate the required expectations. Again, you have simple improper integrals.

--------------------------------------------------------------------------------------------------------------------------

As for the quartiles:

To find the median you need to solve for . The integral is simple to do and the subsequent equation is simple to solve.

The other quartiles are found in a similar way.