Can someone show me how this integrates to 1?

Also, can you show me how to derive the variance and quartiles? Thank you.

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- Feb 26th 2009, 08:34 PMVENIPareto PDF
Can someone show me how this integrates to 1?

Also, can you show me how to derive the variance and quartiles? Thank you. - Feb 27th 2009, 03:09 AMmr fantastic
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.