composition method of generating random variables

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I'm a student learning about methods for generating random variables.

But I'm having a hard time finding examples or youtube tutorials on composition method and algorithm of generating random variables.

Given that this method is grouped with Acceptance-Rejection and inverse transform in the lecture notes my prof handed out, I'd imagine it is a rather common method. So I was wondering whether it is referred to with a different name more commonly? Because I had to no trouble finding examples and tutorials for the A-R and I-T methods.

Obviously my prof's lectures/office hours aren't very helpful and this method isn't even in the textbook. There are no solved examples on this and multiple questions in the homework. Only a single slide in the notes.

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I even searched for different methods of generating RVs () But it seems to not exist.

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