Can someone show me how this integrates to 1?
Also, can you show me how to derive the variance and quartiles? Thank you.
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.
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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.
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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.