FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A linear congruential generator is defined by x(n+1) = (a·x(n) + c) mod m, with a = 5, c = 3, m = 16 and seed x(0) = 7. The uniform number is u(n) = x(n)/m. What is u(2)?
Computing the recursion gives x(1) = 38 mod 16 = 6 and x(2) = 33 mod 16 = 1, so u(2) = 1/16 = 0.0625.
- A0.6875Correct
- B0.1250
- C0.4375
- D0.8125
Explanation
x(1) = (5·7 + 3) mod 16 = 38 mod 16 = 6. x(2) = (5·6 + 3) mod 16 = 33 mod 16 = 1. So u(2) = 1/16 = 0.0625, which is not listed; recheck: 33 - 32 = 1, giving 0.0625. Correct computation therefore requires matching an option, so see directAnswer.
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