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Mabybe this question is duplicate of my other question here : Is PDF always given when we do sampling?

So what I've learned is that, when we already know the exact formula of PDF, we can calcuate any statistics that we want to know.

But I also know that, the purpose of sampling is to estimate properties of probability distributions.

So my conclusion for the question of "Purpose of sampling when we already know the exact PDF formula of the distribution" is, when we know exact formula of PDF, sampling is worthless job.

I know that my conclusion is wrong but I don't know where did I got wrong.

Can anybody help me?

Young Hyun Yoo
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    I think one purpose could be that, even if we know a PDF, it’s not necessarily easy to compute the integral required to find the expected value of our random variable. So you can generate a sample from the distribution of your random variable then compute the mean of the sample to estimate the expected value of your random variable. – littleO Mar 10 '22 at 03:59
  • @littleO So its about the computational cost... :) Thank you for your comment – Young Hyun Yoo Mar 10 '22 at 04:06

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