Question

I am given a function rand5() that generates, with a uniform distribution, a random integer in the closed interval [1,5]. How can I use rand5(), and nothing else, to create a function rand7(), which generates integers in [1,7] (again, uniformly distributed) ?

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1. I searched stackoverflow, and found many similar questions, but not exactly like this one.
2. My initial attempt was rand5() + 0.5*rand5() + 0.5*rand5(). But this won’t generate integers from 1 to 7 with uniform probability. Any answers, or links to answers, are very welcome.

Answer 1

ok I had to think about it for a while but it is actually not that hard. Imagine instead of rand5 you had rand2 which either outputs 0 or 1. You can make rand2 our of rand5 by simply doing

rand2() {
    if(rand5() > 2.5) return 1
    else return 0
}

now using rand2 multiple times do a tree to get rand7. For example if you start rand7 can be in [1,2,3,4,5,6,7] after a throw of rand2 which gives 0 you now subset to [1,2,3,4] and after another throw or rand2 which is 1 you subset to [3,4] and a final throw of 1 gives the output of rand7 to be 4. In general this tree trick can work to take a rand2 and map to randx where x is any integer.