This makes sense and all but isn't there already libraries that will gives us an RV in a desired distribution? For example, in python you can use numpy.random.desired probabilitydistribition

et-yao

That's probably how they work on the inside, which is always very nice to know.

stecen

I was having trouble grasping the intuition on how this step 2 here would generate samples according to the original PDF distribution, because the CDF encodes the "likelihood" to sample all numbers <= x, rather than the likelihood of actually sampling the number x. So in my incorrect mental model, if this method were to generate many samples of x, it wouldn't be because x itself has high "mass" in the pdf, but because all numbers <= x have high "mass" in the pdf. But now I've worked out an example for a uniform pdf on paper and am trying to convince myself that this intuition extends to all pdfs.

This makes sense and all but isn't there already libraries that will gives us an RV in a desired distribution? For example, in python you can use numpy.random.desired probabilitydistribition

That's probably how they work on the inside, which is always very nice to know.

I was having trouble grasping the intuition on how this step 2 here would generate samples according to the original PDF distribution, because the CDF encodes the "likelihood" to sample all numbers <= x, rather than the likelihood of actually sampling the number x. So in my incorrect mental model, if this method were to generate many samples of x, it wouldn't be because x itself has high "mass" in the pdf, but because all numbers <= x have high "mass" in the pdf. But now I've worked out an example for a uniform pdf on paper and am trying to convince myself that this intuition extends to all pdfs.