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How can we know beforehand at what f looks like and what p should be?


Do we start with a complete understanding of f and p?


How do we figure out what p should be if we don't know exactly what f looks like when sampling?


Is there a way to do this dynamically, i.e. if our function is just an input stream of data points?


How did we derive the graphs of f and p?


Is there a specific way that we can know p if we do not know what exactly is f like?


I am still a little confused. Where does this probability distribution p come from? Does it depend on the function f or the material of the object?


I am confused with why this works. If you can have a good estimate of p(x), doesn't this also mean that you have an estimate of f(x) and you can just solve for the integral?


How do we get f and p specifically?


After we switch our sample distribution, the biasness has not changed right? What about consistency?