Company/Two-Sigma

Problem Using a function rand7() that returns an integer from 1 to 7 (inclusive) with uniform probability, implement a function rand5() that returns an integer from 1 to 5 (inclusive) Solution Method 1 - Using rejection sampling The idea is to use rand7() to generate numbers from 1 to 7, and map these numbers to values between [1, 5]. We need to ensure that the probabilities remain uniform despite the discrepancy between the range of 7 and 5, and we can use acceptance-rejection method to avoid bias. ...

Problem Write a method to generate a random number between 1 and 7, given a method that generates a random number between 1 and 5. (i.e., implement rand7() using rand5()). OR Using a function rand5() that returns an integer from 1 to 5 (inclusive) with uniform probability, implement a function rand7() that returns an integer from 1 to 7 (inclusive). Solution This appear to be one of those probabilistic analysis questions. You should be familiar with the concept of expected value, as it could be extremely helpful in probabilistic analysis. ...